Here is a screencast that demonstrates how to build and run tests using .NET 1.1 from inside Visual Studio 2005 using TestDriven.NET 2.0. Under the covers this functionality uses MSBee (MSBuild Extras Toolkit for .NET 1.1) to build target assemblies that are compatible with .NET 1.1. Any build errors and warnings are merged into the 'Error List'. After the solution is built, the target tests are executed using the .NET 1.1 runtime.
You can find the screencast here.
I'd like to thank Craig Lichtenstein for me giving lots of useful feedback as this feature was being developed. Craig used to work on MSBee when he was part of the devdiv developer solutions team.