diff --git a/src/keyboard_drag_strategy.ts b/src/keyboard_drag_strategy.ts
index f9e5fd93..91889670 100644
--- a/src/keyboard_drag_strategy.ts
+++ b/src/keyboard_drag_strategy.ts
@@ -4,24 +4,143 @@
  * SPDX-License-Identifier: Apache-2.0
  */
 
-import {dragging, utils} from 'blockly';
+import {ASTNode, BlockSvg, RenderedConnection, dragging, utils} from 'blockly';
 import {Direction, getDirectionFromXY} from './drag_direction';
+import {LineCursor} from './line_cursor';
 
+// Copied in from core because it is not exported.
+interface ConnectionCandidate {
+  /** A connection on the dragging stack that is compatible with neighbour. */
+  local: RenderedConnection;
+
+  /** A nearby connection that is compatible with local. */
+  neighbour: RenderedConnection;
+
+  /** The distance between the local connection and the neighbour connection. */
+  distance: number;
+}
+
+// @ts-expect-error overrides a private function.
 export class KeyboardDragStrategy extends dragging.BlockDragStrategy {
+  /** Which direction the current constrained drag is in, if any. */
   private currentDragDirection: Direction | null = null;
 
+  /** Where a constrained movement should start when traversing the tree. */
+  private searchNode: ASTNode | null = null;
+
   override startDrag(e?: PointerEvent) {
     super.startDrag(e);
     // Set position of the dragging block, so that it doesn't pop
     // to the top left of the workspace.
     // @ts-expect-error block and startLoc are private.
     this.block.moveDuringDrag(this.startLoc);
+    // @ts-expect-error startParentConn is private.
+    this.searchNode = ASTNode.createConnectionNode(this.startParentConn);
   }
 
   override drag(newLoc: utils.Coordinate, e?: PointerEvent): void {
     if (!e) return;
     this.currentDragDirection = getDirectionFromXY({x: e.tiltX, y: e.tiltY});
     super.drag(newLoc);
+
+    // Handle the case when an unconstrained drag found a connection candidate.
+    // The next constrained move will resume the search from the current candidate
+    // location.
+    // @ts-expect-error connectionCandidate is private.
+    if (this.connectionCandidate) {
+      this.searchNode = ASTNode.createConnectionNode(
+        // @ts-expect-error connectionCandidate is private.
+        (this.connectionCandidate as ConnectionCandidate).neighbour,
+      );
+    }
+  }
+
+  /**
+   * Returns the next compatible connection in keyboard navigation order,
+   * based on the input direction.
+   * Always resumes the search at the last valid connection that was tried.
+   *
+   * @param draggingBlock The block where the drag started.
+   * @returns A valid connection candidate, or null if none was found.
+   */
+  private getConstrainedConnectionCandidate(
+    draggingBlock: BlockSvg,
+  ): ConnectionCandidate | null {
+    // TODO(#385): Make sure this works for any cursor, not just LineCursor.
+    const cursor = draggingBlock.workspace.getCursor() as LineCursor;
+
+    const initialNode = this.searchNode;
+    if (!initialNode || !cursor) return null;
+
+    // @ts-expect-error getLocalConnections is private.
+    const localConns = this.getLocalConnections(draggingBlock);
+    const connectionChecker = draggingBlock.workspace.connectionChecker;
+
+    let candidateConnection: ConnectionCandidate | null = null;
+
+    let potential: ASTNode | null = initialNode;
+    while (potential && !candidateConnection) {
+      if (
+        this.currentDragDirection === Direction.Up ||
+        this.currentDragDirection === Direction.Left
+      ) {
+        potential = cursor.getPreviousNode(potential, (node) => {
+          // @ts-expect-error isConnectionType is private.
+          return node && ASTNode.isConnectionType(node.getType());
+        });
+      } else if (
+        this.currentDragDirection === Direction.Down ||
+        this.currentDragDirection === Direction.Right
+      ) {
+        potential = cursor.getNextNode(potential, (node) => {
+          // @ts-expect-error isConnectionType is private.
+          return node && ASTNode.isConnectionType(node.getType());
+        });
+      }
+
+      localConns.forEach((conn: RenderedConnection) => {
+        const potentialLocation =
+          potential?.getLocation() as RenderedConnection;
+        if (
+          connectionChecker.canConnect(conn, potentialLocation, true, Infinity)
+        ) {
+          candidateConnection = {
+            local: conn,
+            neighbour: potentialLocation,
+            distance: 0,
+          };
+        }
+      });
+    }
+    if (candidateConnection) {
+      this.searchNode = ASTNode.createConnectionNode(
+        (candidateConnection as ConnectionCandidate).neighbour,
+      );
+    }
+    return candidateConnection;
+  }
+
+  override currCandidateIsBetter(
+    currCandidate: ConnectionCandidate,
+    delta: utils.Coordinate,
+    newCandidate: ConnectionCandidate,
+  ): boolean {
+    if (this.isConstrainedMovement()) {
+      return false; // New connection is always better during a constrained drag.
+    }
+    // @ts-expect-error currCandidateIsBetter is private.
+    return super.currCandidateIsBetter(currCandidate, delta, newCandidate);
+  }
+
+  override getConnectionCandidate(
+    draggingBlock: BlockSvg,
+    delta: utils.Coordinate,
+  ): ConnectionCandidate | null {
+    if (this.isConstrainedMovement()) {
+      return this.getConstrainedConnectionCandidate(draggingBlock);
+    }
+    // @ts-expect-error getConnctionCandidate is private.
+    return super.getConnectionCandidate(draggingBlock, delta);
   }
 
   /**
diff --git a/src/line_cursor.ts b/src/line_cursor.ts
index b810ddf9..8bc1fa9d 100644
--- a/src/line_cursor.ts
+++ b/src/line_cursor.ts
@@ -314,7 +314,7 @@ export class LineCursor extends Marker {
    *     should be traversed.
    * @returns The next node in the traversal.
    */
-  private getNextNode(
+  getNextNode(
     node: ASTNode | null,
     isValid: (p1: ASTNode | null) => boolean,
   ): ASTNode | null {
@@ -347,7 +347,7 @@ export class LineCursor extends Marker {
    * @returns The previous node in the traversal or null if no previous node
    *     exists.
    */
-  private getPreviousNode(
+  getPreviousNode(
     node: ASTNode | null,
     isValid: (p1: ASTNode | null) => boolean,
   ): ASTNode | null {