No, to the best of my knowledge there isn't anything comparable to Azul or Zing for .NET.
Part of what Azul got started with was making proprietary CPUs that were optimized for the Java JVM. Here is a good video about that, and why the x86 / x64 architecture has some ... issues in modern use.
However, that proprietary hardware product doesn't seem successful in the market. So I guess that Zing could fairly be described as a strategy pivot for Azul: Their original plan was to sell proprietary hardware with a matching highly optimized JVM. Now they're focused on leveraging their optimized JVM, and sell that for use on regular x86 machines.
@Gamlor is right that one of the main selling points of Zing is "hitless garbage collection", or garbage collection which doesn't make the JVM pause. I'm not aware of anyone pushing that for .NET. Perhaps this answer regarding .NET vs Java GC is interesting.
You could fairly say that Mono is a competing VM for .NET. But to the best of my knowledge, nobody is really selling Mono on being dramatically faster or more scalable than Microsoft .NET.