How to allow only 1 incoming TCPSocket connection?

Am I right that a ServerSocket would allow multiple incoming connections while the TCPSocket would ignore other attempts to connect to it until the connection is closed or disconnected? I am using the socket to transmit data retrieved through a serial port and trying to open a serial port a second time is guaranteed to cause an error.

Yes. A TCPSocket represents a single connection, and even after the connection is closed it will not allow another connection unless you call its Listen method.