diff --git a/.github/workflows/ci.yaml b/.github/workflows/ci.yaml
index 36edb3b..e2782b0 100644
--- a/.github/workflows/ci.yaml
+++ b/.github/workflows/ci.yaml
@@ -56,7 +56,7 @@ jobs:
       XZ_VERSION: ${{ steps.extract.outputs.XZ_VERSION }}
 
     steps:
-    - uses: actions/checkout@v4.1.7
+    - uses: actions/checkout@v5
 
     - name: Extract config variables
       id: extract
@@ -84,7 +84,7 @@ jobs:
         echo "XZ_VERSION=${XZ_VERSION}" | tee -a ${GITHUB_OUTPUT}
 
   build:
-    runs-on: macOS-latest
+    runs-on: macOS-15
     needs: [ config ]
     strategy:
       fail-fast: false
@@ -92,7 +92,16 @@ jobs:
         platform: ['macOS', 'iOS', 'tvOS', 'watchOS', 'visionOS']
 
     steps:
-    - uses: actions/checkout@v4.1.7
+    - uses: actions/checkout@v5
+
+    - name: Set up Xcode
+      # GitHub recommends explicitly selecting the desired Xcode version:
+      # https://github.com/actions/runner-images/issues/12541#issuecomment-3083850140
+      # This became a necessity as a result of
+      # https://github.com/actions/runner-images/issues/12541 and
+      # https://github.com/actions/runner-images/issues/12751.
+      run: |
+        sudo xcode-select --switch /Applications/Xcode_16.4.app
 
     - name: Set up Python
       uses: actions/setup-python@v5.6.0
@@ -117,7 +126,7 @@ jobs:
 
   briefcase-testbed:
     name: Briefcase testbed (${{ matrix.platform }})
-    runs-on: macOS-latest
+    runs-on: macOS-15
     needs: [ config, build ]
     strategy:
       fail-fast: false
@@ -127,10 +136,19 @@ jobs:
             - briefcase-run-args:
 
             - platform: iOS
-              briefcase-run-args: ' -d "iPhone SE (3rd generation)"'
+              briefcase-run-args: ' -d "iPhone 16e::iOS 18.5"'
 
     steps:
-    - uses: actions/checkout@v4.1.7
+    - uses: actions/checkout@v5
+
+    - name: Set up Xcode
+      # GitHub recommends explicitly selecting the desired Xcode version:
+      # https://github.com/actions/runner-images/issues/12541#issuecomment-3083850140
+      # This became a necessity as a result of
+      # https://github.com/actions/runner-images/issues/12541 and
+      # https://github.com/actions/runner-images/issues/12751.
+      run: |
+        sudo xcode-select --switch /Applications/Xcode_16.4.app
 
     - name: Get build artifact
       uses: actions/download-artifact@v5.0.0
@@ -149,7 +167,7 @@ jobs:
         # It's an edge case, but when a new alpha is released, we need to use it ASAP.
         check-latest: true
 
-    - uses: actions/checkout@v4.1.7
+    - uses: actions/checkout@v5
       with:
         repository: beeware/Python-support-testbed
         path: Python-support-testbed
@@ -160,21 +178,25 @@ jobs:
         python -m pip install git+https://github.com/beeware/briefcase.git
 
     - name: Run support testbed check
-      timeout-minutes: 10
+      timeout-minutes: 15
       working-directory: Python-support-testbed
       run: briefcase run ${{ matrix.platform }} Xcode --test ${{ matrix.briefcase-run-args }} -C support_package=\'../dist/Python-${{ needs.config.outputs.PYTHON_VER }}-${{ matrix.platform }}-support.${{ needs.config.outputs.BUILD_NUMBER }}.tar.gz\'
 
   cpython-testbed:
     name: CPython testbed (${{ matrix.platform }})
-    runs-on: macOS-latest
+    # For now, CPython testbed can't run on macos-15: https://github.com/actions/runner-images/issues/12777
+    runs-on: macOS-14
     needs: [ config, build ]
     strategy:
       fail-fast: false
       matrix:
         platform: ["iOS", "visionOS"]
+        include:
+          - platform: "iOS"
+            testbed-args: '--simulator "iPhone 16e,arch=arm64,OS=18.5"'
 
     steps:
-    - uses: actions/checkout@v4.1.7
+    - uses: actions/checkout@v5
 
     - name: Get build artifact
       uses: actions/download-artifact@v5.0.0
@@ -200,7 +222,7 @@ jobs:
         tar zxvf ../../../dist/Python-${{ needs.config.outputs.PYTHON_VER }}-${{ matrix.platform }}-support.${{ needs.config.outputs.BUILD_NUMBER }}.tar.gz
 
     - name: Run CPython testbed
-      timeout-minutes: 10
+      timeout-minutes: 15
       working-directory: support/${{ needs.config.outputs.PYTHON_VER }}/${{ matrix.platform }}
       run: |
         # Run a representative subset of CPython core tests:
@@ -230,7 +252,7 @@ jobs:
             multiarch: arm64-iphoneos
 
     steps:
-    - uses: actions/checkout@v4.1.7
+    - uses: actions/checkout@v5
 
     - name: Get build artifact
       uses: actions/download-artifact@v5.0.0
diff --git a/.github/workflows/publish.yaml b/.github/workflows/publish.yaml
index 587abe8..f913f7d 100644
--- a/.github/workflows/publish.yaml
+++ b/.github/workflows/publish.yaml
@@ -8,7 +8,7 @@ jobs:
   publish:
     runs-on: ubuntu-latest
     steps:
-    - uses: actions/checkout@v4
+    - uses: actions/checkout@v5
 
     - name: Set up Python environment
       uses: actions/setup-python@v5.6.0