Your options are pretty much:
1. Use something like SWIG as Colin mentioned, it basically is automatically creating bindings for you. Personally I don't like added project dependencies.
2. Use C++/CLI to talk directly between your core and your GUI platform. This isn't so bad, but does introduce essentially a third language with its own syntax that is different from C++ and C#. We do this at work (our apps are a blend between native and managed, and we have a lot of C++/CLI going on).
3. Write a C-API to essentially wrap your C++ objects, then use P/Invoke to call those. How much interaction is really going to go on between your core system and the GUI? A small C wrapper to call into probably is enough.
4. COM as DvDMan mentioned...which I wouldn't do for this, the above solutions in my opinion are more desirable.
Personally I'd go with #2 or #3 (leaning on the latter since it doesn't require learning anything new from what I presume you already know), if you wanted to write your core system in C++. But honestly, if I was doing this, both the core system and GUI would be all C#. E.g. use SharpDX for graphics.
Edited by Starnick, 03 April 2014 - 08:11 AM.