diff --git a/pyproject.toml b/pyproject.toml
index e6c63c4d010..fd4a4293882 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -336,7 +336,8 @@ filterwarnings = [
   "default:the `pandas.MultiIndex` object:FutureWarning:xarray.tests.test_variable",
   "default:Using a non-tuple sequence for multidimensional indexing is deprecated:FutureWarning",
   "default:Duplicate dimension names present:UserWarning:xarray.namedarray.core",
-
+  # TODO: this is raised for vlen-utf8, consolidated metadata, U1 dtype
+  "ignore:is currently not part .* the Zarr version 3 specification.",
   # TODO: remove once we know how to deal with a changed signature in protocols
   "default:::xarray.tests.test_strategies",
 ]
diff --git a/xarray/tests/test_backends.py b/xarray/tests/test_backends.py
index 560090e122c..79aa2027ca5 100644
--- a/xarray/tests/test_backends.py
+++ b/xarray/tests/test_backends.py
@@ -2435,10 +2435,16 @@ def test_warning_on_bad_chunks(self) -> None:
         for chunks in good_chunks:
             kwargs = {"chunks": chunks}
             with assert_no_warnings():
-                with self.roundtrip(original, open_kwargs=kwargs) as actual:
-                    for k, v in actual.variables.items():
-                        # only index variables should be in memory
-                        assert v._in_memory == (k in actual.dims)
+                with warnings.catch_warnings():
+                    warnings.filterwarnings(
+                        "ignore",
+                        message=".*Zarr version 3 specification.*",
+                        category=UserWarning,
+                    )
+                    with self.roundtrip(original, open_kwargs=kwargs) as actual:
+                        for k, v in actual.variables.items():
+                            # only index variables should be in memory
+                            assert v._in_memory == (k in actual.dims)
 
     @requires_dask
     def test_deprecate_auto_chunk(self) -> None:
@@ -2985,8 +2991,14 @@ def test_save_emptydim(self, chunk) -> None:
     def test_no_warning_from_open_emptydim_with_chunks(self) -> None:
         ds = Dataset({"x": (("a", "b"), np.empty((5, 0)))}).chunk({"a": 1})
         with assert_no_warnings():
-            with self.roundtrip(ds, open_kwargs=dict(chunks={"a": 1})) as ds_reload:
-                assert_identical(ds, ds_reload)
+            with warnings.catch_warnings():
+                warnings.filterwarnings(
+                    "ignore",
+                    message=".*Zarr version 3 specification.*",
+                    category=UserWarning,
+                )
+                with self.roundtrip(ds, open_kwargs=dict(chunks={"a": 1})) as ds_reload:
+                    assert_identical(ds, ds_reload)
 
     @pytest.mark.parametrize("consolidated", [False, True, None])
     @pytest.mark.parametrize("compute", [False, True])
diff --git a/xarray/tests/test_variable.py b/xarray/tests/test_variable.py
index f4f353eda7d..c3de2253186 100644
--- a/xarray/tests/test_variable.py
+++ b/xarray/tests/test_variable.py
@@ -1108,6 +1108,7 @@ def test_0d_str(self):
         assert v.dtype == np.dtype("S3")
         assert v.values == "foo".encode("ascii")
 
+    @pytest.mark.filterwarnings("ignore:Converting non-nanosecond")
     def test_0d_datetime(self):
         v = Variable([], pd.Timestamp("2000-01-01"))
         assert v.dtype == np.dtype("datetime64[ns]")
@@ -1954,6 +1955,7 @@ def test_big_endian_reduce(self):
         expected = Variable([], 5)
         assert_identical(expected, v.sum())
 
+    @pytest.mark.filterwarnings("ignore:Converting non-nanosecond")
     def test_reduce_funcs(self):
         v = Variable("x", np.array([1, np.nan, 2, 3]))
         assert_identical(v.mean(), Variable([], 2))