diff --git a/xarray/compat/array_api_compat.py b/xarray/compat/array_api_compat.py
index e1e5d5c5bdc..63a7cd8ac44 100644
--- a/xarray/compat/array_api_compat.py
+++ b/xarray/compat/array_api_compat.py
@@ -1,7 +1,20 @@
+import datetime as dt
+
 import numpy as np
 
 from xarray.namedarray.pycompat import array_type
 
+builtin_types = (
+    bool,
+    int,
+    float,
+    complex,
+    str,
+    bytes,
+    dt.datetime,
+    dt.timedelta,
+)
+
 
 def is_weak_scalar_type(t):
     return isinstance(t, bool | int | float | complex | str | bytes)
@@ -38,12 +51,15 @@ def _future_array_api_result_type(*arrays_and_dtypes, xp):
 
 
 def result_type(*arrays_and_dtypes, xp) -> np.dtype:
-    if xp is np or any(
-        isinstance(getattr(t, "dtype", t), np.dtype) for t in arrays_and_dtypes
-    ):
-        return xp.result_type(*arrays_and_dtypes)
-    else:
-        return _future_array_api_result_type(*arrays_and_dtypes, xp=xp)
+    try:
+        if xp is np or any(
+            isinstance(getattr(t, "dtype", t), np.dtype) for t in arrays_and_dtypes
+        ):
+            return xp.result_type(*arrays_and_dtypes)
+        else:
+            return _future_array_api_result_type(*arrays_and_dtypes, xp=xp)
+    except TypeError:
+        return np.dtype(object)
 
 
 def get_array_namespace(*values):
diff --git a/xarray/core/dtypes.py b/xarray/core/dtypes.py
index bb2fe26d727..1e9a69ea977 100644
--- a/xarray/core/dtypes.py
+++ b/xarray/core/dtypes.py
@@ -278,17 +278,11 @@ def should_promote_to_object(
     """
     np_result_types = set()
     for arr_or_dtype in arrays_and_dtypes:
-        try:
-            result_type = array_api_compat.result_type(
-                maybe_promote_to_variable_width(arr_or_dtype), xp=xp
-            )
-            if isinstance(result_type, np.dtype):
-                np_result_types.add(result_type)
-        except TypeError:
-            # passing individual objects to xp.result_type (i.e., what `array_api_compat.result_type` calls) means NEP-18 implementations won't have
-            # a chance to intercept special values (such as NA) that numpy core cannot handle.
-            # Thus they are considered as types that don't need promotion i.e., the `arr_or_dtype` that rose the `TypeError` will not contribute to `np_result_types`.
-            pass
+        result_type = array_api_compat.result_type(
+            maybe_promote_to_variable_width(arr_or_dtype), xp=xp
+        )
+        if isinstance(result_type, np.dtype):
+            np_result_types.add(result_type)
 
     if np_result_types:
         for left, right in PROMOTE_TO_OBJECT:
@@ -328,6 +322,7 @@ def result_type(
 
     if should_promote_to_object(arrays_and_dtypes, xp):
         return np.dtype(object)
+
     maybe_promote = functools.partial(
         maybe_promote_to_variable_width,
         # let extension arrays handle their own str/bytes
diff --git a/xarray/core/utils.py b/xarray/core/utils.py
index 100c256fa9d..f94487759c2 100644
--- a/xarray/core/utils.py
+++ b/xarray/core/utils.py
@@ -213,7 +213,7 @@ def maybe_coerce_to_str(index, original_coords):
 
     try:
         result_type = dtypes.result_type(*original_coords)
-    except (TypeError, ValueError):
+    except ValueError:
         pass
     else:
         if result_type.kind in "SU":
diff --git a/xarray/tests/test_dtypes.py b/xarray/tests/test_dtypes.py
index 4ed66509725..5a772b1691f 100644
--- a/xarray/tests/test_dtypes.py
+++ b/xarray/tests/test_dtypes.py
@@ -32,6 +32,10 @@ class DummyArrayAPINamespace:
         ([np.dtype("<U2"), str], np.dtype("U")),
         ([np.dtype("S3"), np.bytes_], np.dtype("S")),
         ([np.dtype("S10"), bytes], np.dtype("S")),
+        ([type("Foo", (object,), {"foo": "bar"})()], np.object_),
+        ([np.float32, type("Foo", (object,), {"foo": "bar"})()], np.object_),
+        ([np.str_, type("Foo", (object,), {"foo": "bar"})()], np.object_),
+        ([np.bytes_, type("Foo", (object,), {"foo": "bar"})()], np.object_),
     ],
 )
 def test_result_type(args, expected) -> None: