diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml
index 84a157e3b..12f4139c1 100644
--- a/.github/workflows/tests.yml
+++ b/.github/workflows/tests.yml
@@ -15,8 +15,11 @@ jobs:
       matrix:
         # when adding new versions, update the one used to test 
         # friend projects below to the latest one
-        python-version: ["3.8", "3.9", "3.10", "3.11", "3.12"]
+        python-version: ["3.8", "3.9", "3.10", "3.11", "3.12", "3.13"]
         os: [ubuntu-latest, macos-latest, windows-latest]
+        exclude:
+          # TODO Add Windows when regex wheel available for 3.13
+          - {os: windows-latest, python-version: "3.13"}
     steps:
       - uses: actions/checkout@v3
       - name: Set up Python ${{ matrix.python-version }}
@@ -33,7 +36,7 @@ jobs:
       - name: Install sphinx-lint to pull dependencies
         run: python -m pip install -v .
       - name: Download more tests from friend projects
-        if: matrix.python-version == '3.12' && matrix.os == 'ubuntu-latest'
+        if: matrix.python-version == '3.13' && matrix.os == 'ubuntu-latest'
         run: sh download-more-tests.sh
       - name: run tests
         run: python -m pytest
diff --git a/sphinxlint/cli.py b/sphinxlint/cli.py
index f9b12b38e..55d2bdaf5 100644
--- a/sphinxlint/cli.py
+++ b/sphinxlint/cli.py
@@ -138,7 +138,7 @@ def job_count(values):
     try:
         enabled_checkers = {all_checkers[name] for name in enabled_checkers_names}
     except KeyError as err:
-        print(f"Unknown checker: {err.args[0]}.")
+        print(f"Unknown checker: {err.args[0]}.", file=sys.stderr)
         sys.exit(2)
     return enabled_checkers, args
 
@@ -195,7 +195,7 @@ def print_errors(errors):
     """Print errors (or a message if nothing is to be printed)."""
     qty = 0
     for error in errors:
-        print(error)
+        print(error, file=sys.stderr)
         qty += 1
     if qty == 0:
         print("No problems found.")
@@ -221,7 +221,7 @@ def main(argv=None):
 
     for path in args.paths:
         if not os.path.exists(path):
-            print(f"Error: path {path} does not exist")
+            print(f"Error: path {path} does not exist", file=sys.stderr)
             return 2
 
     todo = [
diff --git a/tests/test_sphinxlint.py b/tests/test_sphinxlint.py
index acba51593..85b08afaa 100644
--- a/tests/test_sphinxlint.py
+++ b/tests/test_sphinxlint.py
@@ -29,8 +29,8 @@ def test_sphinxlint_shall_trigger_false_positive(file, capsys):
     assert not has_errors
     has_errors = main(["sphinxlint.py", "--enable", "all", str(file)])
     out, err = capsys.readouterr()
-    assert err == ""
     assert out != "No problems found.\n"
+    assert err != ""
     assert has_errors
 
 
@@ -54,17 +54,17 @@ def test_sphinxlint_shall_not_pass(file, expected_errors, capsys):
     has_errors = main(["sphinxlint.py", "--enable", "all", file])
     out, err = capsys.readouterr()
     assert out != "No problems found.\n"
-    assert err == ""
+    assert err != ""
     assert has_errors
     assert expected_errors, (
         "That's not OK not to tell which errors are expected, "
         """add one using a ".. expect: " line."""
     )
     for expected_error in expected_errors:
-        assert expected_error in out
+        assert expected_error in err
     number_of_expected_errors = len(expected_errors)
-    number_of_reported_errors = len(out.splitlines())
-    assert number_of_expected_errors == number_of_reported_errors, f"{number_of_reported_errors=}, {out=}"
+    number_of_reported_errors = len(err.splitlines())
+    assert number_of_expected_errors == number_of_reported_errors, f"{number_of_reported_errors=}, {err=}"
 
 
 @pytest.mark.parametrize("file", [str(FIXTURE_DIR / "paragraphs.rst")])
@@ -84,8 +84,8 @@ def test_paragraphs(file):
 def test_line_no_in_error_msg(file, capsys):
     has_errors = main(["sphinxlint.py", file])
     out, err = capsys.readouterr()
-    assert err == ""
-    assert "paragraphs.rst:76: role missing colon before" in out
-    assert "paragraphs.rst:70: role use a single backtick" in out
-    assert "paragraphs.rst:65: inline literal missing (escaped) space" in out
+    assert out == ""
+    assert "paragraphs.rst:76: role missing colon before" in err
+    assert "paragraphs.rst:70: role use a single backtick" in err
+    assert "paragraphs.rst:65: inline literal missing (escaped) space" in err
     assert has_errors