I am considering writing a new software product. Performance will be critical, so I am wary of using an interpreted or language or one that uses a emulation layer (read java).

Which leads me to thinking of using C (or C++) however these are both rather long in the tooth. I haven't used either for a long time. I figured in the last 20 years someone has probably created something which is reasonably popular, nice to code in and compiled.

What more modern alternatives are there to C for writing high performance compiled code? 

If C++ is a different beast than it was 15 years ago, I would consider it, I guess I had an assumption that it had some inherent problems.

Parallelisation would be important, but probably not across multiple machines.

There is a language in development called The Rust Programming Language which pursues similar goals as C++ does, notably zero-cost abstractions and fine control over memory management. That said, it is perhaps the most notable upcoming candidate despite being still very young. 

Apart from Rust there really aren't any other popular alternatives which compile to native code. There's Delphi and D too, of course, but they aren't as fast, popular or used. Google's Go language could be a candidate, but it's still very young and aims for a bit different domain.

However, do note that C#(assuming Microsoft platform) and Java might not be all that slow even though they run on top of a virtual machine; the just-in-time compilation of code can do some optimizations which traditional ahead-of-time compilers aren't capable of applying due to lack of information of the program state and environment.

Frankly I would personally not consider C to be a candidate if C++ is an option, mainly because of the fact that modern C++ is safer, works at higher level of abstraction, is more expressive and has practically no performance loss over C(in some cases C++ is notably faster). Simply put, C++ provides everything that C provides and more. Most of the C functionality is considered to be "deprecated" and better, safer, faster and more intuitive alternatives are provided by the C++ standard library.
