Currently TextMate is written in mostly C++ and Objective-C++ (not sure if there’s any pure Objective-C). If one would contribute something larger to TextMate, something that makes sense to put in a new file, can we use something other? The obvious candidate is Swift. The major downside of using Swift is that it doesn’t support interoperability with C++ (but it looks like it might in the future [1]).
As a wildcard, I can mention the D programming language [2]. It’s the only language I know that can interface with both Objective-C and C++. The downside with D would be that the interoperability with Objective-C is lacking some features.