This is a full-featured, free (freedom and beer) interconnect between Mathematica and Matlab. Conversely, this is Wolfram's own commercial solution for connecting Modelica models to Mathematica. Is there a free alternative? None of my searches have found one. I'd be more than happy with something that imports model governing equations.
I'll preface with the fact that I'm a developer for SystemModeler.
There are a number of other Modelica tools on the market, some of them free. They all have their various strength and weaknesses.
The only one that has a connection to Mathematica is SystemModeler, as far as I'm aware.
You could probably build your own link between Mathematica and one of the other tools, but it would be something you would have to do from scratch, utilizing any APIs the tool of your choice happens to have available.
Edit: Starting with Mathematica 11.3, some system modeling functionality comes built-in, without needing to buy SystemModeler. SystemModeler remains as a graphical tool for modeling and simulation.