TestSwarm doesn't have any support for sending notifications, and its really not the scope of the project to provide those.

There are plenty continous integration tools with excellent support for notifications, among them Jenkins. We've got a plugin for Jenkins, which is still a bit rough around the edges, but actually works: Jenkins-TestSwarm plugin

TODO

• Improve plugin output
• put link to testswarm on frontpage of a build
• provide output for tests that Jenkins understands
• Via Test Anything Protocol (TAP)? 
• Via JUnit/Ant xml? See informal spec here and schema (xsd) here