I built a system, starting with a desktop app, 15 years ago when Java was still in its infancy and not ready for use in building these kinds of apps. I knew I needed to have a core in C++ and designed it from the start to be cross platform, including using sized types (eg int32 instead of int or long), so it could run on Mac, Windows, and UNIX (pre-Linux days).
At the time I tried to look for a good cross-platform UI environment, there were a few then including XVT. I went through the training for XVT and when I started to build a real app, I realized that I wasn't going to be able to create a clean, native look and feel on the platform (starting with the Mac). So I gave up that idea and built a native Mac (PowerPlant) UI on top of the portable core.
A couple of years later, we moved onto Windows (UI in MFC). It was faster building a UI the second time around, we maintained a Mac and Windows UI in parallel for a short time and then went all over to Windows. The core later moved onto various flavors of UNIX and Linux, to allow us to run server-based computations. The core did port well, with some adjustments when we made it 64-bit ready.
Now I am back to using a Mac and I wish we could come back to the Mac, but the size and complexity of the app makes this a hard choice. It still makes sense for much of this app to be a desktop app - it is like a CAD environment. But rather than building the UI again in a platform-specific C/C++ language (and continue to maintain an MFC-based UI), I am more inclined to rewrite the entire stack in Java so it can run on multiple platforms.
There may still be reasons to run a non-Java core, say C++ as we did. But I would be wanting to run early performance tests to see if that was really required. And I would be looking carefully at my UI to see if I could be building it as a web app, connected to the core via web services, so I could have a range of clients - desktop apps, mobile apps, web apps, etc. If I needed a piece in C or C++, could it be written under a layer of Java? Or as a web service?
Another consideration - how long will your app be around? How complex will it grow to be? If you have any ideas about this, consider the possible longevity of any UI libraries you are using and your ability over time to have people help maintain them. This may be hard to consider now but worth a thought.