Testing API rate limiting with Postman and Jetpacks

I am trying to set up a test suite using Postman and Jetpacks, for an API I am running. I'm kind of stuck testing the rate limiting. A part of it is pretty easy, inspecting the X-RateLimit headers. But I would like to run tests on the response given, when the limit is actually exceeded.

Does anyone know of a good way to do this?