Depending on what testing framework you are using (MSTest, NUnit etc) I doubt there is a specific 'web interface' for it.
You'd, more than likely, need to get yourself into the continuous integration world, and grab yourself a CI solution.
TeamCity, Jenkins, CruiseControl.NET are all good free (some limitations on TeamCity's free license) CI software. It will be a learning curve, but will be able to give you a nice interface about what tests are running, when they fail, how long they take etc - all in a nice report.
It also, wouldn't be that hard to write something like this yourself. The reports that NUnit etc make are all well documented & standardised XML. Thus, it wouldn't take much to take the information you need and shove it into a nice report.