diff --git a/.github/workflows/release.yml b/.github/workflows/release.yml
index 4a00bf8fc..ed52ddd80 100644
--- a/.github/workflows/release.yml
+++ b/.github/workflows/release.yml
@@ -56,7 +56,7 @@ jobs:
       with:
         platforms: all
     - name: Build wheels
-      uses: pypa/cibuildwheel@v2.16.2
+      uses: pypa/cibuildwheel@v2.20.0
       env:
         BUILD_EXTENSION: yes
     - name: Save wheels
diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml
index 15a45bdfb..b9172b7fb 100644
--- a/.github/workflows/tests.yml
+++ b/.github/workflows/tests.yml
@@ -62,6 +62,7 @@ jobs:
           - "3.10"
           - "3.11"
           - "3.12"
+          - "3.13"
           - "pypy-3.9"
           - "pypy-3.10"
         is_main:
@@ -78,6 +79,7 @@ jobs:
       uses: actions/setup-python@v5
       with:
         python-version: ${{ matrix.python }}
+        allow-prereleases: true
     - name: Install tox
       run: pip install tox
     - name: Run tests
diff --git a/docs/faq/misc.rst b/docs/faq/misc.rst
index ee5ad2372..0e74a784f 100644
--- a/docs/faq/misc.rst
+++ b/docs/faq/misc.rst
@@ -3,6 +3,9 @@ Miscellaneous
 
 .. currentmodule:: websockets
 
+.. Remove this question when dropping Python < 3.13, which provides natively
+.. a good error message in this case.
+
 Why do I get the error: ``module 'websockets' has no attribute '...'``?
 .......................................................................
 
diff --git a/docs/project/changelog.rst b/docs/project/changelog.rst
index 8143e3483..00b055dd1 100644
--- a/docs/project/changelog.rst
+++ b/docs/project/changelog.rst
@@ -71,7 +71,7 @@ New features
     See :func:`websockets.asyncio.client.connect` and
     :func:`websockets.asyncio.server.serve` for details.
 
-* Validated compatibility with Python 3.12.
+* Validated compatibility with Python 3.12 and 3.13.
 
 * Added :doc:`environment variables <../reference/variables>` to configure debug
   logs, the ``Server`` and ``User-Agent`` headers, as well as security limits.
diff --git a/pyproject.toml b/pyproject.toml
index de8acd6a3..c1d34c90b 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -24,6 +24,7 @@ classifiers = [
     "Programming Language :: Python :: 3.10",
     "Programming Language :: Python :: 3.11",
     "Programming Language :: Python :: 3.12",
+    "Programming Language :: Python :: 3.13",
 ]
 dynamic = ["version", "readme"]
 
diff --git a/src/websockets/asyncio/connection.py b/src/websockets/asyncio/connection.py
index 152c6789e..4f44d798c 100644
--- a/src/websockets/asyncio/connection.py
+++ b/src/websockets/asyncio/connection.py
@@ -564,8 +564,7 @@ async def ping(self, data: Data | None = None) -> Awaitable[None]:
 
             pong_waiter = self.loop.create_future()
             # The event loop's default clock is time.monotonic(). Its resolution
-            # is a bit low on Windows (~16ms). We cannot use time.perf_counter()
-            # because it doesn't count time elapsed while the process sleeps.
+            # is a bit low on Windows (~16ms). This is improved in Python 3.13.
             ping_timestamp = self.loop.time()
             self.pong_waiters[data] = (pong_waiter, ping_timestamp)
             self.protocol.send_ping(data)
diff --git a/tox.ini b/tox.ini
index 1edcfe261..16d9c9f16 100644
--- a/tox.ini
+++ b/tox.ini
@@ -5,6 +5,7 @@ env_list =
     py310
     py311
     py312
+    py313
     coverage
     black
     ruff