At the time, twitter allowed you to receive SMS notifications of tweets posted to a followed account. I created a private account and used twitter's API to post tweets to with the notification content I wanted to send. I then had "dummy" accounts follow the "notification" account. These dummy accounts had recipient phone numbers with SMS notifications turned on.
The flow was: Web App -> Twitter API -> Tweet from "notification" account -> followers received SMS notifications. Free SMS delivery!
It was clunky and SMS notifications looked like they came from twitter (they did) but it solved my use case perfectly.