diff --git a/pandas/tests/indexing/multiindex/test_partial.py b/pandas/tests/indexing/multiindex/test_partial.py
index 9c356b81b85db2..c203d986efd23f 100644
--- a/pandas/tests/indexing/multiindex/test_partial.py
+++ b/pandas/tests/indexing/multiindex/test_partial.py
@@ -178,9 +178,9 @@ def test_partial_loc_missing(self, multiindex_year_month_day_dataframe_random_da
         # assert (self.ymd.loc[2000]['A'] == 0).all()
 
         # Pretty sure the second (and maybe even the first) is already wrong.
-        with pytest.raises(Exception):
+        with pytest.raises(KeyError, match="6"):
             ymd.loc[(2000, 6)]
-        with pytest.raises(Exception):
+        with pytest.raises(KeyError, match="(2000, 6)"):
             ymd.loc[(2000, 6), 0]
 
     # ---------------------------------------------------------------------
diff --git a/pandas/tests/indexing/test_coercion.py b/pandas/tests/indexing/test_coercion.py
index 15f58006426f49..41f967ce327968 100644
--- a/pandas/tests/indexing/test_coercion.py
+++ b/pandas/tests/indexing/test_coercion.py
@@ -331,7 +331,8 @@ def test_setitem_index_float64(self, val, exp_dtype, request):
         if exp_dtype is IndexError:
             # float + int -> int
             temp = obj.copy()
-            with pytest.raises(exp_dtype):
+            msg = "index 5 is out of bounds for axis 0 with size 4"
+            with pytest.raises(exp_dtype, match=msg):
                 temp[5] = 5
             mark = pytest.mark.xfail(reason="TODO_GH12747 The result must be float")
             request.node.add_marker(mark)