diff --git a/.github/workflows/daily.yml b/.github/workflows/daily.yml
index 7949f351f5f9..be0d5b7cad71 100644
--- a/.github/workflows/daily.yml
+++ b/.github/workflows/daily.yml
@@ -66,7 +66,7 @@ jobs:
       - uses: actions/checkout@v4
       - uses: actions/setup-python@v5
         with:
-          python-version: "3.12"
+          python-version: "3.13"
           cache: pip
           cache-dependency-path: |
             requirements-tests.txt
diff --git a/.github/workflows/stubtest_third_party.yml b/.github/workflows/stubtest_third_party.yml
index 8e7105b9ddf0..69ec7c6ac625 100644
--- a/.github/workflows/stubtest_third_party.yml
+++ b/.github/workflows/stubtest_third_party.yml
@@ -41,7 +41,7 @@ jobs:
           fetch-depth: 0
       - uses: actions/setup-python@v5
         with:
-          python-version: "3.12"
+          python-version: "3.13"
           cache: pip
           cache-dependency-path: |
             requirements-tests.txt
diff --git a/stubs/corus/METADATA.toml b/stubs/corus/METADATA.toml
index f966ab456995..e7cf25599620 100644
--- a/stubs/corus/METADATA.toml
+++ b/stubs/corus/METADATA.toml
@@ -1,2 +1,6 @@
 version = "0.10.*"
 upstream_repository = "https://github.com/natasha/corus"
+
+[tool.stubtest]
+# As of version 0.10.0, corus doesn't support Python 3.13.
+skip = true
diff --git a/stubs/humanfriendly/METADATA.toml b/stubs/humanfriendly/METADATA.toml
index c8518e705021..eaca32d94d25 100644
--- a/stubs/humanfriendly/METADATA.toml
+++ b/stubs/humanfriendly/METADATA.toml
@@ -3,3 +3,5 @@ upstream_repository = "https://github.com/xolox/python-humanfriendly"
 
 [tool.stubtest]
 stubtest_requirements = ["docutils", "mock"]
+# Package is unsupported and doesn't support Python 3.13 as of 2025-03-17.
+skip = true
diff --git a/stubs/passlib/@tests/stubtest_allowlist.txt b/stubs/passlib/@tests/stubtest_allowlist.txt
index 16ec9f5109a1..c953253672cd 100644
--- a/stubs/passlib/@tests/stubtest_allowlist.txt
+++ b/stubs/passlib/@tests/stubtest_allowlist.txt
@@ -90,3 +90,8 @@ passlib.utils.compat.*
 
 # Tests are not included:
 passlib.tests.*
+
+# This is only available when the crypt module is available. This module
+# was dropped from the standard library of Python 3.13, but is still available
+# in some environments.
+(passlib.hosts.host_context)?
diff --git a/stubs/pygit2/METADATA.toml b/stubs/pygit2/METADATA.toml
index 13eec7dc9537..8f0525f88186 100644
--- a/stubs/pygit2/METADATA.toml
+++ b/stubs/pygit2/METADATA.toml
@@ -5,3 +5,5 @@ obsolete_since = "1.16.0" # Released on 2024-10-11
 
 [tool.stubtest]
 platforms = ["darwin", "linux", "win32"]
+# Does not build on any platform on Python 3.13 as of 2025-03-17.
+skip = true
diff --git a/stubs/tensorflow/METADATA.toml b/stubs/tensorflow/METADATA.toml
index 66c658d2a6ce..94d4b9f8a08b 100644
--- a/stubs/tensorflow/METADATA.toml
+++ b/stubs/tensorflow/METADATA.toml
@@ -10,3 +10,6 @@ partial_stub = true
 ignore_missing_stub = true
 # TODO: Support/update to keras 3.7
 stubtest_requirements = ["keras==3.6.*"]
+# tensorflow 2.19 doesn't support Python 3.13:
+# https://github.com/tensorflow/tensorflow/issues/78774
+skip = true
diff --git a/stubs/tqdm/@tests/stubtest_allowlist.txt b/stubs/tqdm/@tests/stubtest_allowlist.txt
index ca237a8d068d..e14a351b27a6 100644
--- a/stubs/tqdm/@tests/stubtest_allowlist.txt
+++ b/stubs/tqdm/@tests/stubtest_allowlist.txt
@@ -6,3 +6,7 @@ tqdm._tqdm_notebook.__all__
 
 # Cannot import in stubtest
 tqdm.__main__
+
+# TODO: Reenable when tensorflow supports Python 3.13 and is added to the
+# stubtest dependencies in METADATA.toml.
+tqdm.keras
diff --git a/stubs/tqdm/METADATA.toml b/stubs/tqdm/METADATA.toml
index fddf4c03eb49..f218397eb207 100644
--- a/stubs/tqdm/METADATA.toml
+++ b/stubs/tqdm/METADATA.toml
@@ -4,4 +4,7 @@ requires = ["types-requests"]
 
 [tool.stubtest]
 extras = ["slack", "telegram"]
-stubtest_requirements = ["dask", "pandas", "rich", "tensorflow"]
+# Add `"tensorflow"` to this list when there's a tensorflow release supporting
+# Python 3.13: https://github.com/tensorflow/tensorflow/issues/78774.
+# Also remove tqdm.keras from @tests/stubtest_allowlist.txt.
+stubtest_requirements = ["dask", "pandas", "rich"]
diff --git a/stubs/tree-sitter-languages/METADATA.toml b/stubs/tree-sitter-languages/METADATA.toml
index 055b8d94dd38..b139562018f3 100644
--- a/stubs/tree-sitter-languages/METADATA.toml
+++ b/stubs/tree-sitter-languages/METADATA.toml
@@ -1,3 +1,9 @@
 version = "1.10.*"
 upstream_repository = "https://github.com/grantjenks/py-tree-sitter-languages"
 requires = ["tree-sitter>=0.20.3"]
+
+[tool.stubtest]
+# This package is unmaintained and doesn't support Python 3.13.
+# See https://github.com/grantjenks/py-tree-sitter-languages/issues/75 and
+# https://github.com/grantjenks/py-tree-sitter-languages/blob/main/README.rst#status
+skip = true