I've narrowed down the secret sauce to build JUCE-based projects in TravisCI, with clang on Linux.
Basically, the only variable I've needed to change up is the path to the Makefile.
The reason for creating a README is to get the the boilerplate TravisCI hook pre-setup with just a variable to change.
Side note: the TravisCI file could certainly be added to JUCE, and tweaked to build the Unit Test Runner with clang on Linux, and GCC I believe.
(This has been completed. See this post: http://www.juce.com/forum/topic/adding-continuous-integration-support-juce-travisci )