The recommended API for Stomp and messaging in general on .Net / C# is NMS which provides a standard API to Stomp, Apache ActiveMQ, MSMQ and other messaging systems.
This .Net client for Stomp is written in C# so it should work on any Mono or MS platform. It was written by Joe Walnes.
You can grab it in SVN here...
We've currently got NUnit tests for it as well; though we still need NAnt builds for it.