My guess at this point is that there's no way of launching a Web application in the WP8 emulator directly from Visual Studio 2012. The jury's still out on how to start the emulator application from Windows 8 (i.e. not via Visual Studio) though :(
The only way I'm currently able to start the WP8 emulator is to launch a WP8 app in it from Visual Studio 2012.
The workaround I've found is to debug a WP8 app in the emulator via Visual Studio, stop debugging while not closing the emulator, open the Web app project in Visual studio, start it and navigate to it in the WP8 emulator.
Note that you must provide your computer's IP address to the browser, as the emulated WP8 is running as a separate host on the network. As such, you must also configure IIS Express to allow access via said IP address and also configure the firewall to let HTTP traffic on the port in question through.