How can I add log messages to an NUnit test that will appear in a nant build execution?

NUnit 3's way of logging during a test is via the TestContext class. It has a raft of static Write variants. Each emits general content to the test result.

TestContext.Out yields a TextWriter that can also be used to emit logging information into test results.

Console.WriteLine() should be preserved (it is for my version of NUnit at least).

That said, consider - each time you want to add some text output - how you could turn it into an assertion with a message. Your tests will get much better.