diff --git a/sklearn/ensemble/_hist_gradient_boosting/gradient_boosting.py b/sklearn/ensemble/_hist_gradient_boosting/gradient_boosting.py
index 31069fe14ee41..23e76b4307b6f 100644
--- a/sklearn/ensemble/_hist_gradient_boosting/gradient_boosting.py
+++ b/sklearn/ensemble/_hist_gradient_boosting/gradient_boosting.py
@@ -1165,7 +1165,15 @@ def _compute_partial_dependence_recursion(self, grid, target_features):
         return averaged_predictions
 
     def _more_tags(self):
-        return {"allow_nan": True}
+        return {
+            "allow_nan": True,
+            "_xfail_checks": {
+                "check_estimators_pickle": (
+                    "The memory views of the nodes parameter need to be defined"
+                    "as read only in the Cython implementation."
+                ),
+            },
+        }
 
     @abstractmethod
     def _get_loss(self, sample_weight):
diff --git a/sklearn/preprocessing/_polynomial.py b/sklearn/preprocessing/_polynomial.py
index 46be5d2c13bbc..9e09715a50718 100644
--- a/sklearn/preprocessing/_polynomial.py
+++ b/sklearn/preprocessing/_polynomial.py
@@ -936,3 +936,13 @@ def transform(self, X):
             # We chose the last one.
             indices = [j for j in range(XBS.shape[1]) if (j + 1) % n_splines != 0]
             return XBS[:, indices]
+
+    def _more_tags(self):
+        return {
+            "_xfail_checks": {
+                "check_estimators_pickle": (
+                    "Current Scipy implementation of _bsplines does not"
+                    "support const memory views."
+                ),
+            }
+        }
diff --git a/sklearn/utils/estimator_checks.py b/sklearn/utils/estimator_checks.py
index bbfd12ad39b9c..9eb666c68984d 100644
--- a/sklearn/utils/estimator_checks.py
+++ b/sklearn/utils/estimator_checks.py
@@ -129,6 +129,7 @@ def _yield_checks(estimator):
     # Test that estimators can be pickled, and once pickled
     # give the same answer as before.
     yield check_estimators_pickle
+    yield partial(check_estimators_pickle, readonly_memmap=True)
 
     yield check_estimator_get_tags_default_keys
 
@@ -1870,7 +1871,7 @@ def check_nonsquare_error(name, estimator_orig):
 
 
 @ignore_warnings
-def check_estimators_pickle(name, estimator_orig):
+def check_estimators_pickle(name, estimator_orig, readonly_memmap=False):
     """Test that we can pickle all estimators."""
     check_methods = ["predict", "transform", "decision_function", "predict_proba"]
 
@@ -1899,16 +1900,19 @@ def check_estimators_pickle(name, estimator_orig):
     set_random_state(estimator)
     estimator.fit(X, y)
 
-    # pickle and unpickle!
-    pickled_estimator = pickle.dumps(estimator)
-    module_name = estimator.__module__
-    if module_name.startswith("sklearn.") and not (
-        "test_" in module_name or module_name.endswith("_testing")
-    ):
-        # strict check for sklearn estimators that are not implemented in test
-        # modules.
-        assert b"version" in pickled_estimator
-    unpickled_estimator = pickle.loads(pickled_estimator)
+    if readonly_memmap:
+        unpickled_estimator = create_memmap_backed_data(estimator)
+    else:
+        # pickle and unpickle!
+        pickled_estimator = pickle.dumps(estimator)
+        module_name = estimator.__module__
+        if module_name.startswith("sklearn.") and not (
+            "test_" in module_name or module_name.endswith("_testing")
+        ):
+            # strict check for sklearn estimators that are not implemented in test
+            # modules.
+            assert b"version" in pickled_estimator
+        unpickled_estimator = pickle.loads(pickled_estimator)
 
     result = dict()
     for method in check_methods: