diff --git a/build.rs b/build.rs
index 493c8b0b74f..29610e593b8 100644
--- a/build.rs
+++ b/build.rs
@@ -33,6 +33,7 @@ struct InterpreterConfig {
     base_prefix: String,
     executable: String,
     machine: String,
+    maxsize_bits: Option<u32>,
 }
 
 #[derive(Deserialize, Debug, Clone, PartialEq)]
@@ -181,6 +182,7 @@ fn load_cross_compile_info() -> Result<(InterpreterConfig, HashMap<String, Strin
         base_prefix: "".to_string(),
         executable: "".to_string(),
         machine: "".to_string(),
+        maxsize_bits: None,
     };
 
     Ok((interpreter_config, fix_config_map(config_map)))
@@ -456,7 +458,8 @@ print(json.dumps({
     "base_prefix": base_prefix,
     "shared": PYPY or bool(sysconfig.get_config_var('Py_ENABLE_SHARED')),
     "executable": sys.executable,
-    "machine": platform.machine()
+    "machine": platform.machine(),
+    "maxsize_bits": sys.maxsize.bit_length(),
 }))
 "#;
     let json = run_python_script(interpreter, script)?;
@@ -475,7 +478,7 @@ fn configure(interpreter_config: &InterpreterConfig) -> Result<String> {
         }
     }
 
-    check_target_architecture(&interpreter_config.machine)?;
+    check_target_architecture(interpreter_config)?;
 
     let is_extension_module = env::var_os("CARGO_FEATURE_EXTENSION_MODULE").is_some();
     if !is_extension_module || cfg!(target_os = "windows") {
@@ -517,32 +520,39 @@ fn configure(interpreter_config: &InterpreterConfig) -> Result<String> {
     Ok(flags)
 }
 
-fn check_target_architecture(python_machine: &str) -> Result<()> {
+fn check_target_architecture(interpreter_config: &InterpreterConfig) -> Result<()> {
     // Try to check whether the target architecture matches the python library
-    let target_arch = match env::var("CARGO_CFG_TARGET_ARCH")
-        .as_ref()
-        .map(|e| e.as_str())
-    {
-        Ok("x86_64") => Some("64-bit"),
-        Ok("x86") => Some("32-bit"),
-        _ => None, // It might be possible to recognise other architectures, this will do for now.
+    let rust_target = match env::var("CARGO_CFG_TARGET_POINTER_WIDTH")?.as_str() {
+        "64" => "64-bit",
+        "32" => "32-bit",
+        x => bail!("unexpected Rust target pointer width: {}", x),
     };
 
-    let python_arch = match python_machine {
-        "AMD64" | "x86_64" => Some("64-bit"),
-        "i686" | "x86" => Some("32-bit"),
-        _ => None, // It might be possible to recognise other architectures, this will do for now.
+    // Why are we using at sys.maxsize here, rather than just
+    // platform.architecture()? Because the latter can give weird results on
+    // macOS. See https://stackoverflow.com/a/1405971/823869.
+    let python_target = match interpreter_config.maxsize_bits {
+        // sys.maxsize is a signed value, so it's one bit shorter than the
+        // pointer width.
+        Some(63) => "64-bit",
+        Some(31) => "32-bit",
+        None => {
+            // Unset, e.g. because we're cross-compiling. Don't check anything
+            // in this case.
+            return Ok(());
+        }
+        Some(n) => bail!("unexpected Python maxsize_bits: {}", n),
     };
 
-    match (target_arch, python_arch) {
-        // If we could recognise both, and they're different, fail.
-        (Some(t), Some(p)) if p != t => bail!(
+    if rust_target != python_target {
+        bail!(
             "Your Rust target architecture ({}) does not match your python interpreter ({})",
-            t,
-            p
-        ),
-        _ => Ok(()),
+            rust_target,
+            python_target
+        );
     }
+
+    Ok(())
 }
 
 fn check_rustc_version() -> Result<()> {