So, the question is how to configure Web role on Azure Compute Emulator to work like on local IIS? By this I mean, that, the web role have the fixed url (like you can in project
Check out this solution from Michael Collier [a fellow Windows Azure MVP]
The answer is that you cannot run it on a static port, but it should run on the first available port in its port range (starting at 80 and incrementing until it finds a free port). If it increments with every "debug" session starting, then it's because the previous emulator didnt teardown completely before you started a new one.
There are some ideas how to fix this issue here: http://social.msdn.microsoft.com/Forums/en/windowsazuredevelopment/thread/ae2df7e0-5005-4bcd-8b69-bb53323eb589