diff --git a/cibuildwheel/architecture.py b/cibuildwheel/architecture.py
index 7b90ff947..a922f6f53 100644
--- a/cibuildwheel/architecture.py
+++ b/cibuildwheel/architecture.py
@@ -3,12 +3,19 @@
 import functools
 import platform as platform_module
 import re
+import sys
 from enum import Enum
 
 from .typing import Final, Literal, PlatformName, assert_never
 
 PRETTY_NAMES: Final = {"linux": "Linux", "macos": "macOS", "windows": "Windows"}
 
+ARCH_SYNONYMS: Final[list[dict[PlatformName, str | None]]] = [
+    {"linux": "x86_64", "macos": "x86_64", "windows": "AMD64"},
+    {"linux": "i686", "macos": None, "windows": "x86"},
+    {"linux": "aarch64", "macos": "arm64", "windows": "ARM64"},
+]
+
 
 @functools.total_ordering
 class Architecture(Enum):
@@ -56,14 +63,37 @@ def parse_config(config: str, platform: PlatformName) -> set[Architecture]:
 
     @staticmethod
     def auto_archs(platform: PlatformName) -> set[Architecture]:
-        native_architecture = Architecture(platform_module.machine())
+        native_machine = platform_module.machine()
+
+        # Cross-platform support. Used for --print-build-identifiers or docker builds.
+        host_platform: PlatformName = (
+            "windows"
+            if sys.platform.startswith("win")
+            else ("macos" if sys.platform.startswith("darwin") else "linux")
+        )
+
+        native_architecture = Architecture(native_machine)
+
+        # we might need to rename the native arch to the machine we're running
+        # on, as the same arch can have different names on different platforms
+        if host_platform != platform:
+            for arch_synonym in ARCH_SYNONYMS:
+                if native_machine == arch_synonym.get(host_platform):
+                    synonym = arch_synonym[platform]
+
+                    if synonym is None:
+                        # can't build anything on this platform
+                        return set()
+
+                    native_architecture = Architecture(synonym)
+
         result = {native_architecture}
 
-        if platform == "linux" and native_architecture == Architecture.x86_64:
+        if platform == "linux" and Architecture.x86_64 in result:
             # x86_64 machines can run i686 containers
             result.add(Architecture.i686)
 
-        if platform == "windows" and native_architecture == Architecture.AMD64:
+        if platform == "windows" and Architecture.AMD64 in result:
             result.add(Architecture.x86)
 
         return result
diff --git a/unit_test/architecture_test.py b/unit_test/architecture_test.py
new file mode 100644
index 000000000..1c7efd2ee
--- /dev/null
+++ b/unit_test/architecture_test.py
@@ -0,0 +1,82 @@
+from __future__ import annotations
+
+import platform as platform_module
+import sys
+
+import pytest
+
+from cibuildwheel.architecture import Architecture
+
+
+@pytest.fixture(
+    params=[
+        pytest.param(("linux", "linux", "x86_64", "64"), id="linux-64"),
+        pytest.param(("linux", "linux", "i686", "32"), id="linux-32"),
+        pytest.param(("linux", "linux", "aarch64", "arm"), id="linux-arm"),
+        pytest.param(("macos", "darwin", "x86_64", "64"), id="macos-64"),
+        pytest.param(("macos", "darwin", "arm64", "arm"), id="macos-arm"),
+        pytest.param(("windows", "win32", "x86", "32"), id="windows-32"),
+        pytest.param(("windows", "win32", "AMD64", "64"), id="windows-64"),
+        pytest.param(("windows", "win32", "ARM64", "arm"), id="windows-arm"),
+    ]
+)
+def platform_machine(request, monkeypatch):
+    platform_name, platform_value, machine_value, machine_name = request.param
+    monkeypatch.setattr(sys, "platform", platform_value)
+    monkeypatch.setattr(platform_module, "machine", lambda: machine_value)
+    return platform_name, machine_name
+
+
+def test_arch_auto(platform_machine):
+    platform_name, machine_name = platform_machine
+
+    arch_set = Architecture.auto_archs("linux")
+    expected = {
+        "32": {Architecture.i686},
+        "64": {Architecture.x86_64, Architecture.i686},
+        "arm": {Architecture.aarch64},
+    }
+    assert arch_set == expected[machine_name]
+
+    arch_set = Architecture.auto_archs("macos")
+    expected = {"32": set(), "64": {Architecture.x86_64}, "arm": {Architecture.arm64}}
+    assert arch_set == expected[machine_name]
+
+    arch_set = Architecture.auto_archs("windows")
+    expected = {
+        "32": {Architecture.x86},
+        "64": {Architecture.AMD64, Architecture.x86},
+        "arm": {Architecture.ARM64},
+    }
+    assert arch_set == expected[machine_name]
+
+
+def test_arch_auto64(platform_machine):
+    platform_name, machine_name = platform_machine
+
+    arch_set = Architecture.parse_config("auto64", "linux")
+    expected = {"32": set(), "64": {Architecture.x86_64}, "arm": {Architecture.aarch64}}
+    assert arch_set == expected[machine_name]
+
+    arch_set = Architecture.parse_config("auto64", "macos")
+    expected = {"32": set(), "64": {Architecture.x86_64}, "arm": {Architecture.arm64}}
+    assert arch_set == expected[machine_name]
+
+    arch_set = Architecture.parse_config("auto64", "windows")
+    expected = {"32": set(), "64": {Architecture.AMD64}, "arm": {Architecture.ARM64}}
+    assert arch_set == expected[machine_name]
+
+
+def test_arch_auto32(platform_machine):
+    platform_name, machine_name = platform_machine
+
+    arch_set = Architecture.parse_config("auto32", "linux")
+    expected = {"32": {Architecture.i686}, "64": {Architecture.i686}, "arm": set()}
+    assert arch_set == expected[machine_name]
+
+    arch_set = Architecture.parse_config("auto32", "macos")
+    assert arch_set == set()
+
+    arch_set = Architecture.parse_config("auto32", "windows")
+    expected = {"32": {Architecture.x86}, "64": {Architecture.x86}, "arm": set()}
+    assert arch_set == expected[machine_name]