For Xbox "servers," you can, technically, build your server feature into the game itself, using some secret cheat code. Then start up an Xbox running the game in server mode. Use regular game matchmaking with a special value for game type, for example, to find the running server, join a session, get the data you need, and then disconnect.
Yes, this is a hack, and it's not the most reliable way to run a game server, but it's totally possible to do using the existing SDK and hardware.