How to close a socket left open by a killed program?

Assume your socket is named s... you need to set socket.SO_REUSEADDR on the server's socket before binding to an interface... this will allow you to immediately restart a TCP server...

s.setsockopt(socket.SOL_SOCKET, socket.SO_REUSEADDR, 1)
s.bind((ADDR, PORT))

You might want to try using Twisted for your networking. Mike gave the correct low-level answer, SO_REUSEADDR, but he didn't mention that this isn't a very good option to set on Windows. This is the sort of thing that Twisted takes care of for you automatically. There are many, many other examples of this kind of boring low-level detail that you have to pay attention to when using the socket module directly but which you can forget about if you use a higher level library like Twisted.

You are confusing sockets, connections, and ports. Sockets are endpoints of connections, which in turn are 5-tuples {protocol, local-ip, local-port, remote-ip, remote-port}. The killed program's socket has been closed by the OS, and ditto the connection. The only relic of the connection is the peer's socket and the corresponding port at the peer host. So what you should really be asking about is how to reuse the local port. To which the answer is SO_REUSEADDR as per the other answers.