diff --git a/pandas/core/indexes/category.py b/pandas/core/indexes/category.py
index 06df8f85cded7..d875cd682030b 100644
--- a/pandas/core/indexes/category.py
+++ b/pandas/core/indexes/category.py
@@ -529,19 +529,11 @@ def get_indexer(self, target, method=None, limit=None, tolerance=None):
         method = missing.clean_reindex_fill_method(method)
         target = ibase.ensure_index(target)
 
+        self._check_indexing_method(method)
+
         if self.is_unique and self.equals(target):
             return np.arange(len(self), dtype="intp")
 
-        if method == "pad" or method == "backfill":
-            raise NotImplementedError(
-                "method='pad' and method='backfill' not "
-                "implemented yet for CategoricalIndex"
-            )
-        elif method == "nearest":
-            raise NotImplementedError(
-                "method='nearest' not implemented yet for CategoricalIndex"
-            )
-
         # Note: we use engine.get_indexer_non_unique below because, even if
         #  `target` is unique, any non-category entries in it will be encoded
         #  as -1 by _get_codes_for_get_indexer, so `codes` may not be unique.
diff --git a/pandas/core/indexes/extension.py b/pandas/core/indexes/extension.py
index 4d09a97b18eed..c117c32f26d25 100644
--- a/pandas/core/indexes/extension.py
+++ b/pandas/core/indexes/extension.py
@@ -230,6 +230,21 @@ def __getitem__(self, key):
 
     # ---------------------------------------------------------------------
 
+    def _check_indexing_method(self, method):
+        """
+        Raise if we have a get_indexer `method` that is not supported or valid.
+        """
+        # GH#37871 for now this is only for IntervalIndex and CategoricalIndex
+        if method is None:
+            return
+
+        if method in ["bfill", "backfill", "pad", "ffill", "nearest"]:
+            raise NotImplementedError(
+                f"method {method} not yet implemented for {type(self).__name__}"
+            )
+
+        raise ValueError("Invalid fill method")
+
     def _get_engine_target(self) -> np.ndarray:
         return np.asarray(self._data)
 
diff --git a/pandas/core/indexes/interval.py b/pandas/core/indexes/interval.py
index 2aec86c9cdfae..e6174c63fbc15 100644
--- a/pandas/core/indexes/interval.py
+++ b/pandas/core/indexes/interval.py
@@ -582,17 +582,6 @@ def _maybe_convert_i8(self, key):
 
         return key_i8
 
-    def _check_method(self, method):
-        if method is None:
-            return
-
-        if method in ["bfill", "backfill", "pad", "ffill", "nearest"]:
-            raise NotImplementedError(
-                f"method {method} not yet implemented for IntervalIndex"
-            )
-
-        raise ValueError("Invalid fill method")
-
     def _searchsorted_monotonic(self, label, side, exclude_label=False):
         if not self.is_non_overlapping_monotonic:
             raise KeyError(
@@ -663,7 +652,7 @@ def get_loc(
         >>> index.get_loc(pd.Interval(0, 1))
         0
         """
-        self._check_method(method)
+        self._check_indexing_method(method)
 
         if not is_scalar(key):
             raise InvalidIndexError(key)
@@ -714,7 +703,7 @@ def get_indexer(
         tolerance: Optional[Any] = None,
     ) -> np.ndarray:
 
-        self._check_method(method)
+        self._check_indexing_method(method)
 
         if self.is_overlapping:
             raise InvalidIndexError(
diff --git a/pandas/tests/indexes/categorical/test_indexing.py b/pandas/tests/indexes/categorical/test_indexing.py
index 9f4b7f7bad10f..cf9360821d37f 100644
--- a/pandas/tests/indexes/categorical/test_indexing.py
+++ b/pandas/tests/indexes/categorical/test_indexing.py
@@ -238,16 +238,14 @@ def test_get_indexer(self):
             r1 = idx1.get_indexer(idx2)
             tm.assert_almost_equal(r1, np.array([0, 1, 2, -1], dtype=np.intp))
 
-        msg = (
-            "method='pad' and method='backfill' not implemented yet for "
-            "CategoricalIndex"
-        )
+        msg = "method pad not yet implemented for CategoricalIndex"
         with pytest.raises(NotImplementedError, match=msg):
             idx2.get_indexer(idx1, method="pad")
+        msg = "method backfill not yet implemented for CategoricalIndex"
         with pytest.raises(NotImplementedError, match=msg):
             idx2.get_indexer(idx1, method="backfill")
 
-        msg = "method='nearest' not implemented yet for CategoricalIndex"
+        msg = "method nearest not yet implemented for CategoricalIndex"
         with pytest.raises(NotImplementedError, match=msg):
             idx2.get_indexer(idx1, method="nearest")