I have an ASP.NET Web API application, with an ApiController that features asynchronous methods, returning Task<> objects and marked with the async<
Bear in mind that the NUnit 2.6 series, like those before it, is built to target the .NET 2.0 framework. So, NUnit can only do the same things you could code yourself, in an assembly targeting .NET 2.0.
Specifically, you can't mark your test method as async and expect NUnit to do anything special with it.
You can, however,
Neither of the above will give you asynchronous test execution, if that's what you are hoping for. No other tests will execute while waiting for the asynchronous operation to complete.
Another option is to use NUnitLite. NUnitLite 0.8 supports the [Asynchronous] attribute which will allow other tests to continue while your asynchronous test completes. The advantage of the attribute is that it allows asynchronous tests to work in .NET 2.0 through 4.0
We don't currently have a .NET 4.5 build of NUnitLite but it will be added soon and we are working on a change that will make use of [Asynchronous] optional in that environment. For now, you can easily download and recompile the source code for .NET 4.5.
For the future, look to NUnit 3.0 to support async methods fully along with general parallel execution of tests on multiple threads or in multiple processes.