diff --git a/.github/workflows/wheels.yml b/.github/workflows/wheels.yml
index a38ec5ee359d9..47ef020bcb5f1 100644
--- a/.github/workflows/wheels.yml
+++ b/.github/workflows/wheels.yml
@@ -162,7 +162,7 @@ jobs:
         run: echo "sdist_name=$(cd ./dist && ls -d */)" >> "$GITHUB_ENV"
 
       - name: Build wheels
-        uses: pypa/cibuildwheel@v2.23.3
+        uses: pypa/cibuildwheel@v3.1.1
         with:
          package-dir: ./dist/${{ startsWith(matrix.buildplat[1], 'macosx') && env.sdist_name || needs.build_sdist.outputs.sdist_file }}
         env:
diff --git a/pandas/tests/extension/test_period.py b/pandas/tests/extension/test_period.py
index 2e6fe12cbbd13..31496c1b7db3d 100644
--- a/pandas/tests/extension/test_period.py
+++ b/pandas/tests/extension/test_period.py
@@ -25,7 +25,6 @@
     Period,
     iNaT,
 )
-from pandas.compat import is_platform_windows
 
 from pandas.core.dtypes.dtypes import PeriodDtype
 
@@ -102,12 +101,10 @@ def check_reduce(self, ser: pd.Series, op_name: str, skipna: bool):
             return super().check_reduce(ser, op_name, skipna)
 
     @pytest.mark.parametrize("periods", [1, -2])
-    def test_diff(self, data, periods):
-        if is_platform_windows():
-            with tm.assert_produces_warning(RuntimeWarning, check_stacklevel=False):
-                super().test_diff(data, periods)
-        else:
-            super().test_diff(data, periods)
+    # NOTE: RuntimeWarning on Windows(non-ARM) platforms (in CI)
+    @pytest.mark.filterwarnings("ignore::RuntimeWarning")
+    def test_diff(self, request, data, periods):
+        super().test_diff(data, periods)
 
     @pytest.mark.parametrize("na_action", [None, "ignore"])
     def test_map(self, data, na_action):
diff --git a/pyproject.toml b/pyproject.toml
index e013222f8fe79..be0060033b201 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -144,7 +144,7 @@ parentdir_prefix = "pandas-"
 setup = ['--vsenv'] # For Windows
 
 [tool.cibuildwheel]
-skip = "cp36-* cp37-* cp38-* cp39-* pp* *_i686 *_ppc64le *_s390x"
+skip = "cp38-* cp39-* *_i686 *_ppc64le *_s390x"
 build-verbosity = 3
 environment = {LDFLAGS="-Wl,--strip-all"}
 test-requires = "hypothesis>=6.84.0 pytest>=7.3.2 pytest-xdist>=3.4.0"
@@ -190,6 +190,8 @@ select = "*pyodide*"
 test-requires = "pytest>=7.3.2 hypothesis>=6.84.0"
 # Pyodide repairs wheels on its own, using auditwheel-emscripten
 repair-wheel-command = ""
+# https://github.com/pyodide/pyodide/issues/5805
+build-verbosity = 1
 test-command = """
   PANDAS_CI='1' python -c 'import pandas as pd; \
   pd.test(extra_args=["-m not clipboard and not single_cpu and not slow and not network and not db", "--no-strict-data-files"]);' \