diff --git a/internal/jsonrpc2/conn.go b/internal/jsonrpc2/conn.go
index 49902b00..5549ee1c 100644
--- a/internal/jsonrpc2/conn.go
+++ b/internal/jsonrpc2/conn.go
@@ -483,10 +483,32 @@ func (c *Connection) Cancel(id ID) {
 
 // Wait blocks until the connection is fully closed, but does not close it.
 func (c *Connection) Wait() error {
+	return c.wait(true)
+}
+
+// wait for the connection to close, and aggregates the most cause of its
+// termination, if abnormal.
+//
+// The fromWait argument allows this logic to be shared with Close, where we
+// only want to expose the closeErr.
+//
+// (Previously, Wait also only returned the closeErr, which was misleading if
+// the connection was broken for another reason).
+func (c *Connection) wait(fromWait bool) error {
 	var err error
 	<-c.done
 	c.updateInFlight(func(s *inFlightState) {
-		err = s.closeErr
+		if fromWait {
+			if !errors.Is(s.readErr, io.EOF) {
+				err = s.readErr
+			}
+			if err == nil && !errors.Is(s.writeErr, io.EOF) {
+				err = s.writeErr
+			}
+		}
+		if err == nil {
+			err = s.closeErr
+		}
 	})
 	return err
 }
@@ -502,8 +524,7 @@ func (c *Connection) Close() error {
 	// Stop handling new requests, and interrupt the reader (by closing the
 	// connection) as soon as the active requests finish.
 	c.updateInFlight(func(s *inFlightState) { s.connClosing = true })
-
-	return c.Wait()
+	return c.wait(false)
 }
 
 // readIncoming collects inbound messages from the reader and delivers them, either responding
diff --git a/mcp/streamable.go b/mcp/streamable.go
index 1eef9a74..3e3cc6f8 100644
--- a/mcp/streamable.go
+++ b/mcp/streamable.go
@@ -1119,6 +1119,17 @@ type streamableClientConn struct {
 	sessionID         string
 }
 
+// errSessionMissing distinguishes if the session is known to not be present on
+// the server (see [streamableClientConn.fail]).
+//
+// TODO(rfindley): should we expose this error value (and its corresponding
+// API) to the user?
+//
+// The spec says that if the server returns 404, clients should reestablish
+// a session. For now, we delegate that to the user, but do they need a way to
+// differentiate a 'NotFound' error from other errors?
+var errSessionMissing = errors.New("session not found")
+
 var _ clientConnection = (*streamableClientConn)(nil)
 
 func (c *streamableClientConn) sessionUpdated(state clientSessionState) {
@@ -1146,6 +1157,10 @@ func (c *streamableClientConn) sessionUpdated(state clientSessionState) {
 //
 // If err is non-nil, it is terminal, and subsequent (or pending) Reads will
 // fail.
+//
+// If err wraps errSessionMissing, the failure indicates that the session is no
+// longer present on the server, and no final DELETE will be performed when
+// closing the connection.
 func (c *streamableClientConn) fail(err error) {
 	if err != nil {
 		c.failOnce.Do(func() {
@@ -1193,9 +1208,19 @@ func (c *streamableClientConn) Write(ctx context.Context, msg jsonrpc.Message) e
 		return err
 	}
 
+	var requestSummary string
+	switch msg := msg.(type) {
+	case *jsonrpc.Request:
+		requestSummary = fmt.Sprintf("sending %q", msg.Method)
+	case *jsonrpc.Response:
+		requestSummary = fmt.Sprintf("sending jsonrpc response #%d", msg.ID)
+	default:
+		panic("unreachable")
+	}
+
 	data, err := jsonrpc.EncodeMessage(msg)
 	if err != nil {
-		return err
+		return fmt.Errorf("%s: %v", requestSummary, err)
 	}
 
 	req, err := http.NewRequestWithContext(ctx, http.MethodPost, c.url, bytes.NewReader(data))
@@ -1208,9 +1233,21 @@ func (c *streamableClientConn) Write(ctx context.Context, msg jsonrpc.Message) e
 
 	resp, err := c.client.Do(req)
 	if err != nil {
+		return fmt.Errorf("%s: %v", requestSummary, err)
+	}
+
+	// Section 2.5.3: "The server MAY terminate the session at any time, after
+	// which it MUST respond to requests containing that session ID with HTTP
+	// 404 Not Found."
+	if resp.StatusCode == http.StatusNotFound {
+		// Fail the session immediately, rather than relying on jsonrpc2 to fail
+		// (and close) it, because we want the call to Close to know that this
+		// session is missing (and therefore not send the DELETE).
+		err := fmt.Errorf("%s: failed to send: %w", requestSummary, errSessionMissing)
+		c.fail(err)
+		resp.Body.Close()
 		return err
 	}
-
 	if resp.StatusCode < 200 || resp.StatusCode >= 300 {
 		resp.Body.Close()
 		return fmt.Errorf("broken session: %v", resp.Status)
@@ -1233,16 +1270,6 @@ func (c *streamableClientConn) Write(ctx context.Context, msg jsonrpc.Message) e
 		return nil
 	}
 
-	var requestSummary string
-	switch msg := msg.(type) {
-	case *jsonrpc.Request:
-		requestSummary = fmt.Sprintf("sending %q", msg.Method)
-	case *jsonrpc.Response:
-		requestSummary = fmt.Sprintf("sending jsonrpc response #%d", msg.ID)
-	default:
-		panic("unreachable")
-	}
-
 	switch ct := resp.Header.Get("Content-Type"); ct {
 	case "application/json":
 		go c.handleJSON(requestSummary, resp)
@@ -1333,6 +1360,11 @@ func (c *streamableClientConn) handleSSE(requestSummary string, initialResp *htt
 			resp.Body.Close()
 			return
 		}
+		// (see equivalent handling in [streamableClientConn.Write]).
+		if resp.StatusCode == http.StatusNotFound {
+			c.fail(fmt.Errorf("%s: failed to reconnect: %w", requestSummary, errSessionMissing))
+			return
+		}
 		if resp.StatusCode < 200 || resp.StatusCode >= 300 {
 			resp.Body.Close()
 			c.fail(fmt.Errorf("%s: failed to reconnect: %v", requestSummary, http.StatusText(resp.StatusCode)))
@@ -1423,13 +1455,17 @@ func (c *streamableClientConn) Close() error {
 		c.cancel()
 		close(c.done)
 
-		req, err := http.NewRequest(http.MethodDelete, c.url, nil)
-		if err != nil {
-			c.closeErr = err
+		if errors.Is(c.failure(), errSessionMissing) {
+			// If the session is missing, no need to delete it.
 		} else {
-			c.setMCPHeaders(req)
-			if _, err := c.client.Do(req); err != nil {
+			req, err := http.NewRequest(http.MethodDelete, c.url, nil)
+			if err != nil {
 				c.closeErr = err
+			} else {
+				c.setMCPHeaders(req)
+				if _, err := c.client.Do(req); err != nil {
+					c.closeErr = err
+				}
 			}
 		}
 	})
diff --git a/mcp/streamable_client_test.go b/mcp/streamable_client_test.go
index fe87b21c..001d3a64 100644
--- a/mcp/streamable_client_test.go
+++ b/mcp/streamable_client_test.go
@@ -29,7 +29,7 @@ type streamableRequestKey struct {
 type header map[string]string
 
 type streamableResponse struct {
-	header              header
+	header              header // response headers
 	status              int    // or http.StatusOK
 	body                string // or ""
 	optional            bool   // if set, request need not be sent
@@ -187,6 +187,56 @@ func TestStreamableClientTransportLifecycle(t *testing.T) {
 	}
 }
 
+func TestStreamableClientRedundantDelete(t *testing.T) {
+	ctx := context.Background()
+
+	// The lifecycle test verifies various behavior of the streamable client
+	// initialization:
+	//  - check that it can handle application/json responses
+	//  - check that it sends the negotiated protocol version
+	fake := &fakeStreamableServer{
+		t: t,
+		responses: fakeResponses{
+			{"POST", "", methodInitialize}: {
+				header: header{
+					"Content-Type":  "application/json",
+					sessionIDHeader: "123",
+				},
+				body: jsonBody(t, initResp),
+			},
+			{"POST", "123", notificationInitialized}: {
+				status:              http.StatusAccepted,
+				wantProtocolVersion: latestProtocolVersion,
+			},
+			{"GET", "123", ""}: {
+				status:   http.StatusMethodNotAllowed,
+				optional: true,
+			},
+			{"POST", "123", methodListTools}: {
+				status: http.StatusNotFound,
+			},
+		},
+	}
+
+	httpServer := httptest.NewServer(fake)
+	defer httpServer.Close()
+
+	transport := &StreamableClientTransport{Endpoint: httpServer.URL}
+	client := NewClient(testImpl, nil)
+	session, err := client.Connect(ctx, transport, nil)
+	if err != nil {
+		t.Fatalf("client.Connect() failed: %v", err)
+	}
+	_, err = session.ListTools(ctx, nil)
+	if err == nil {
+		t.Errorf("Listing tools: got nil error, want non-nil")
+	}
+	_ = session.Wait() // must not hang
+	if missing := fake.missingRequests(); len(missing) > 0 {
+		t.Errorf("did not receive expected requests: %v", missing)
+	}
+}
+
 func TestStreamableClientGETHandling(t *testing.T) {
 	ctx := context.Background()
 
diff --git a/mcp/streamable_test.go b/mcp/streamable_test.go
index a85fbec0..f0da3dc9 100644
--- a/mcp/streamable_test.go
+++ b/mcp/streamable_test.go
@@ -190,6 +190,80 @@ func TestStreamableTransports(t *testing.T) {
 	}
 }
 
+func TestStreamableServerShutdown(t *testing.T) {
+	ctx := context.Background()
+
+	// This test checks that closing the streamable HTTP server actually results
+	// in client session termination, provided one of following holds:
+	//  1. The server is stateful, and therefore the hanging GET fails the connection.
+	//  2. The server is stateless, and the client uses a KeepAlive.
+	tests := []struct {
+		name                 string
+		stateless, keepalive bool
+	}{
+		{"stateful", false, false},
+		{"stateless with keepalive", true, true},
+	}
+
+	for _, test := range tests {
+		t.Run(test.name, func(t *testing.T) {
+			server := NewServer(testImpl, nil)
+			// Add a tool, just so we can check things are working.
+			AddTool(server, &Tool{Name: "greet"}, sayHi)
+
+			handler := NewStreamableHTTPHandler(
+				func(req *http.Request) *Server { return server },
+				&StreamableHTTPOptions{Stateless: test.stateless})
+
+			// When we shut down the server, we need to explicitly close ongoing
+			// connections. Otherwise, the hanging GET may never terminate.
+			httpServer := httptest.NewUnstartedServer(handler)
+			httpServer.Config.RegisterOnShutdown(func() {
+				for session := range server.Sessions() {
+					session.Close()
+				}
+			})
+			httpServer.Start()
+			defer httpServer.Close()
+
+			// Connect and run a tool.
+			var opts ClientOptions
+			if test.keepalive {
+				opts.KeepAlive = 50 * time.Millisecond
+			}
+			client := NewClient(testImpl, &opts)
+			clientSession, err := client.Connect(ctx, &StreamableClientTransport{
+				Endpoint:   httpServer.URL,
+				MaxRetries: -1, // avoid slow tests during exponential retries
+			}, nil)
+			if err != nil {
+				t.Fatal(err)
+			}
+
+			params := &CallToolParams{
+				Name:      "greet",
+				Arguments: map[string]any{"name": "foo"},
+			}
+			// Verify that we can call a tool.
+			if _, err := clientSession.CallTool(ctx, params); err != nil {
+				t.Fatalf("CallTool() failed: %v", err)
+			}
+
+			// Shut down the server. Sessions should terminate.
+			go func() {
+				if err := httpServer.Config.Shutdown(ctx); err != nil && !errors.Is(err, http.ErrServerClosed) {
+					t.Errorf("closing http server: %v", err)
+				}
+			}()
+
+			// Wait may return an error (after all, the connection failed), but it
+			// should not hang.
+			t.Log("Client waiting")
+			_ = clientSession.Wait()
+		})
+	}
+}
+
 // TestClientReplay verifies that the client can recover from a mid-stream
 // network failure and receive replayed messages (if replay is configured). It
 // uses a proxy that is killed and restarted to simulate a recoverable network