In my github repo's readme.md file I have a Travis-CI badge. I use the following link:
The only way to do this would be to pass the link through my own service which would use the github's http referrer header to determine which branch is being referenced and then fetch the appropriate image from Travis CI
I would rather make one Travis-CI badge per branch, for the reader to choose or consider the appropriate when seeing the
Update 2016 (3 years later): while nothing has changed on the GitHub side, fedorqui reports in the workaround mentioned in "Get Travis Shield on Github to Reflect Selected Branch Status" by Andrie.
Simply display all the branches and their respective TravisCI badges.
If you have only two or three branches, that could be enough.