The Autobahn Kit is a great place to start. His 9.x tests provide good performance coverage for different message sizes, fragment sizes, tcp packet sizes, and round-trip times for both client and server implementations. Keep in mind that Autobahn is written in python and, as such, has a reduced ability to provide accurate metrics as your implementation approaches the speed of the test client / server itself.
To provide better performance indicators for implications written in faster languages than Python, I am working on the implementation of many Autobahn 9.x tests using my C ++ WebSocket ++ library . WebSocket ++ also includes a common stress testing client that allows server authors to check what happens to their servers with thousands of connections.
Both Autobahn and WebSocket ++ fully support the final RFC6455 WebSocket specification, released in November 2011. WebSockets is a relatively new technology, and testing tools for them are not yet fully mature. If you have any questions or feedback about WebSocket performance testing, feel free to contact me personally or post to the Github project.
Disclaimer: I am the author of WebSocket ++ and a member of the Autobahn test suite.