diff --git a/CHANGELOG.rst b/CHANGELOG.rst
index 844a10d2..6cf29e6e 100644
--- a/CHANGELOG.rst
+++ b/CHANGELOG.rst
@@ -10,6 +10,8 @@ The third digit is only for regressions.
 Backward-incompatible changes:
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 
+- ``OpenSSL.SSL.Connection.set_session`` now raises ``ValueError`` if the ``Session`` was obtained from a ``Connection`` that was using a different ``Context`` than this one. OpenSSL requires (but does not verify) that sessions only be re-used with a compatible ``SSL_CTX``, so this contract is now enforced.
+
 Deprecations:
 ^^^^^^^^^^^^^
 
diff --git a/src/OpenSSL/SSL.py b/src/OpenSSL/SSL.py
index 90065e95..e951eae6 100644
--- a/src/OpenSSL/SSL.py
+++ b/src/OpenSSL/SSL.py
@@ -847,6 +847,11 @@ class Session:
     """
 
     _session: Any
+    # The Context the Connection this Session came from was using. OpenSSL
+    # requires that a session only be re-used with a compatible SSL_CTX, but
+    # doesn't verify it, so we pin the Context here and enforce identity in
+    # Connection.set_session.
+    _context: Context
 
 
 F = TypeVar("F", bound=Callable[..., Any])
@@ -3032,12 +3037,18 @@ def get_session(self) -> Session | None:
 
         pysession = Session.__new__(Session)
         pysession._session = _ffi.gc(session, _lib.SSL_SESSION_free)
+        pysession._context = self._context
         return pysession
 
     def set_session(self, session: Session) -> None:
         """
         Set the session to be used when the TLS/SSL connection is established.
 
+        The session must have been obtained, via :meth:`get_session`, from a
+        :class:`Connection` that was using the same :class:`Context` as this
+        one. OpenSSL requires (but does not verify) that sessions only be
+        re-used with a compatible ``SSL_CTX``, so this is enforced here.
+
         :param session: A Session instance representing the session to use.
         :returns: None
 
@@ -3046,6 +3057,12 @@ def set_session(self, session: Session) -> None:
         if not isinstance(session, Session):
             raise TypeError("session must be a Session instance")
 
+        if session._context is not self._context:
+            raise ValueError(
+                "session must have been created by a Connection using the "
+                "same Context as this one"
+            )
+
         result = _lib.SSL_set_session(self._ssl, session._session)
         _openssl_assert(result == 1)
 
diff --git a/tests/test_ssl.py b/tests/test_ssl.py
index b3da8a6d..1e6939c3 100644
--- a/tests/test_ssl.py
+++ b/tests/test_ssl.py
@@ -3108,12 +3108,22 @@ def makeServer(socket: socket) -> Connection:
             server.set_accept_state()
             return server
 
-        originalServer, originalClient = loopback(server_factory=makeServer)
+        clientCtx = Context(SSLv23_METHOD)
+
+        def makeOriginalClient(socket: socket) -> Connection:
+            client = Connection(clientCtx, socket)
+            client.set_connect_state()
+            return client
+
+        originalServer, originalClient = loopback(
+            server_factory=makeServer, client_factory=makeOriginalClient
+        )
         originalSession = originalClient.get_session()
         assert originalSession is not None
 
         def makeClient(socket: socket) -> Connection:
-            client = loopback_client_factory(socket)
+            client = Connection(clientCtx, socket)
+            client.set_connect_state()
             client.set_session(originalSession)
             return client
 
@@ -3129,18 +3139,15 @@ def makeClient(socket: socket) -> Connection:
         # connections is the same, the session was re-used!
         assert originalServer.master_key() == resumedServer.master_key()
 
-    def test_set_session_wrong_method(self) -> None:
+    def test_set_session_wrong_context(self) -> None:
         """
-        If `Connection.set_session` is passed a `Session` instance associated
-        with a context using a different SSL method than the `Connection`
-        is using, a `OpenSSL.SSL.Error` is raised.
+        If `Connection.set_session` is passed a `Session` instance that was
+        created by a `Connection` using a different `Context` than the
+        `Connection` is using, a `ValueError` is raised.
         """
-        v1 = TLSv1_2_METHOD
-        v2 = TLSv1_METHOD
-
         key = load_privatekey(FILETYPE_PEM, server_key_pem)
         cert = load_certificate(FILETYPE_PEM, server_cert_pem)
-        ctx = Context(v1)
+        ctx = Context(TLSv1_2_METHOD)
         ctx.use_privatekey(key)
         ctx.use_certificate(cert)
         ctx.set_session_id(b"unity-test")
@@ -3150,26 +3157,15 @@ def makeServer(socket: socket) -> Connection:
             server.set_accept_state()
             return server
 
-        def makeOriginalClient(socket: socket) -> Connection:
-            client = Connection(Context(v1), socket)
-            client.set_connect_state()
-            return client
-
-        _, originalClient = loopback(
-            server_factory=makeServer, client_factory=makeOriginalClient
-        )
+        _, originalClient = loopback(server_factory=makeServer)
         originalSession = originalClient.get_session()
         assert originalSession is not None
 
-        def makeClient(socket: socket) -> Connection:
-            # Intentionally use a different, incompatible method here.
-            client = Connection(Context(v2), socket)
-            client.set_connect_state()
+        # Intentionally use a different Context here.
+        client = Connection(Context(SSLv23_METHOD), None)
+        client.set_connect_state()
+        with pytest.raises(ValueError):
             client.set_session(originalSession)
-            return client
-
-        with pytest.raises(Error):
-            loopback(client_factory=makeClient, server_factory=makeServer)
 
     def test_wantWriteError(self) -> None:
         """