Depending on what you really need to test, it may work to... not use a web server. Check out WWW::Mechanize::Cached.

First you run your tests live on your machine while having the caching function save the pages to files (or some other caching mechanism). Then you can just re-run the test again, essentially in off-line mode since the results will come from disk.

I actually started doing this today when the thing to test wasn't "get web page", but to combine that with some processing.

/J