The Fiddler documentation is poor in regard of configuring the Java RE or SDK to work with Fiddler and HTTPS. After some digging I found this article which helped me solve the problem:
http://codeketchup.blogspot.com/2014/03/how-to-use-eclipse-with-fiddler-step-by.html
It is important to read the comments too, as from the article it is not 100% clear what to do.