Postman founder here. Postman let's you run tests outside of Postman through the newman tool (free) [1]. Just take collections outside Postman and run them anywhere you want. Collections can have Javascript scripts embedded inside them for request chaining (transferring data from one request to another) or just writing integration tests. Tons of possibilities and we have some great new stuff coming up around this.
[1]: http://www.getpostman.com/docs/newman_intro