diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 1be5cf7b..fa954db7 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -49,7 +49,7 @@ jobs:
     strategy:
       fail-fast: false
       matrix:
-        python-version: ["3.7", "pypy-3.9", "3.12"]
+        python-version: ["3.7", "pypy-3.9", "3.12", "3.13"]
         runs-on: [ubuntu-latest, macos-13]
         cmake-version: ["3.15.x"]
 
@@ -93,6 +93,9 @@ jobs:
           - python-version: "3.12"
             runs-on: windows-latest
             cmake-version: "3.26.x"
+          - python-version: "3.13"
+            runs-on: windows-latest
+            cmake-version: "3.26.x"
 
     steps:
       - uses: actions/checkout@v4
@@ -320,7 +323,7 @@ jobs:
     strategy:
       fail-fast: false
       matrix:
-        runs-on: [ubuntu-latest, macos-14, windows-latest]
+        runs-on: [ubuntu-latest, macos-latest, windows-latest]
     runs-on: ${{ matrix.runs-on }}
     timeout-minutes: 15
 
@@ -331,7 +334,7 @@ jobs:
 
       - uses: wntrblm/nox@2024.04.15
         with:
-          python-versions: "3.11"
+          python-versions: "3.12"
 
       - name: Linkcheck
         run: nox -s docs -- -b linkcheck
diff --git a/src/scikit_build_core/builder/sysconfig.py b/src/scikit_build_core/builder/sysconfig.py
index 6ac3b688..47aa6442 100644
--- a/src/scikit_build_core/builder/sysconfig.py
+++ b/src/scikit_build_core/builder/sysconfig.py
@@ -62,7 +62,15 @@ def get_python_library(env: Mapping[str, str], *, abi3: bool = False) -> Path |
 
     libdirstr = sysconfig.get_config_var("LIBDIR")
     ldlibrarystr = sysconfig.get_config_var("LDLIBRARY")
-    librarystr = sysconfig.get_config_var("LDLIBRARY")
+    librarystr = sysconfig.get_config_var("LIBRARY")
+    if abi3:
+        if ldlibrarystr is not None:
+            ldlibrarystr = ldlibrarystr.replace(
+                f"python3{sys.version_info[1]}", "python3"
+            )
+        if librarystr is not None:
+            librarystr = librarystr.replace(f"python3{sys.version_info[1]}", "python3")
+
     libdir: Path | None = libdirstr and Path(libdirstr)
     ldlibrary: Path | None = ldlibrarystr and Path(ldlibrarystr)
     library: Path | None = librarystr and Path(librarystr)