diff --git a/src/cryptography/hazmat/backends/openssl/x509.py b/src/cryptography/hazmat/backends/openssl/x509.py
index fa4d1a0..1de3f4d 100644
--- a/src/cryptography/hazmat/backends/openssl/x509.py
+++ b/src/cryptography/hazmat/backends/openssl/x509.py
@@ -63,6 +63,26 @@
         pkey = self._backend._lib.X509_get_pubkey(self._x509)
         assert pkey != self._backend._ffi.NULL
         pkey = self._backend._ffi.gc(pkey, self._backend._lib.EVP_PKEY_free)
+        # The following check is to find ECDSA certificates with unnamed
+        # curves and raise an error for now.
+        if (
+            self._backend._lib.Cryptography_HAS_EC == 1 and
+            pkey.type == self._backend._lib.EVP_PKEY_EC
+        ):
+            ec_cdata = self._backend._lib.EVP_PKEY_get1_EC_KEY(pkey)
+            assert ec_cdata != self._backend._ffi.NULL
+            ec_cdata = self._backend._ffi.gc(
+                ec_cdata, self._backend._lib.EC_KEY_free
+            )
+            group = self._backend._lib.EC_KEY_get0_group(ec_cdata)
+            assert group != self._backend._ffi.NULL
+            nid = self._backend._lib.EC_GROUP_get_curve_name(group)
+            if nid == self._backend._lib.NID_undef:
+                raise NotImplementedError(
+                    "ECDSA certificates without named curves are unsupported "
+                    "at this time"
+                )
+
         return self._backend._evp_pkey_to_public_key(pkey)
 
     @property
diff --git a/tests/test_x509.py b/tests/test_x509.py
index 638c7d1..7a4d0b7 100644
--- a/tests/test_x509.py
+++ b/tests/test_x509.py
@@ -179,3 +179,13 @@
         )
         public_key = cert.public_key()
         assert isinstance(public_key, interfaces.EllipticCurvePublicKey)
+
+    def test_load_ecdsa_no_named_curve(self, backend):
+        _skip_curve_unsupported(backend, ec.SECP256R1())
+        cert = _load_cert(
+            os.path.join("x509", "custom", "ec_no_named_curve.pem"),
+            x509.load_pem_x509_certificate,
+            backend
+        )
+        with pytest.raises(NotImplementedError):
+            cert.public_key()