In UNIX (Not Windows), an accepted socket consumes a file descriptor, so the limit is the number of open file descriptors allowed. The number of open file descriptors is a per-process limit with both a hard and a soft limit. See ulimit (2) for more information.
Note that if you close the socket, you free the file descriptor, so it can be used over again. The ulimit limit applies only to the number of simultaneous open file descriptors.
To specifically answer your question, there isn't a limit on the number of sockets a port can accept, only on the number that the process listening to the port can have open at the same time. If there were a limit, web servers, who listen on port 80, would have to be restarted more often.