Combinatorial Interaction Testing (CIT) is an effective technique that, however, requires a good tool support in order to be successfully applied. There are several tools and applications for CIT, and most of them are distributed as desktop applications or as special plugins of existing programs and require some installation procedures to be used. Software as a Service (SaaS) paradigm can be applied to CIT modeling and test generation, proving several advantages to the tester. There are already some attempts in this direction, but with some shortcomings (little editing support, for example). In this paper, we present CTWedge (Combinatorial Testing Web EDiting and GEneration), which defines a language for CIT models in the presence of constraints by using Xtext. It introduces a web service for editing CIT specifications and it interfaces, through a server, with other tools for test generation. CTWedge can improve the user experience by providing a complete environment for CIT modeling and generation on the web without sacrificing usability.