diff --git a/test/test_windows.py b/test/test_windows.py
new file mode 100644
index 00000000..95e34998
--- /dev/null
+++ b/test/test_windows.py
@@ -0,0 +1,32 @@
+import pytest
+
+from . import test_projects, utils
+
+basic_project = test_projects.new_c_project()
+
+
+def test_wheel_tag_is_correct_when_using_windows_cross_compile(tmp_path):
+    if utils.platform != "windows":
+        pytest.skip("This test is only relevant to Windows")
+
+    project_dir = tmp_path / "project"
+    basic_project.generate(project_dir)
+
+    # build the wheels
+    actual_wheels = utils.cibuildwheel_run(
+        project_dir,
+        add_env={
+            "CIBW_BUILD": "cp310-*",
+        },
+        add_args=["--platform", "windows", "--archs", "ARM64"]
+    )
+
+    # check that the expected wheels are produced
+    expected_wheels = [
+        "spam-0.1.0-cp310-win_arm64.whl",
+    ]
+
+    print("actual_wheels", actual_wheels)
+    print("expected_wheels", expected_wheels)
+
+    assert set(actual_wheels) == set(expected_wheels)