resizable serial console window?

When using the serial console of my system I always end up with $COLUMNS=80 and $LINES=24. While I can change these variables manually it is somewhat annoying to do this any time when the client side terminal window has been resized. Usually I'm connecting to the console using screen /dev/mytty baudrate. Changing the $TERM environment variable to "screen" or "xterm" does not help. Will I need to call getty with some of those instead of vt100? Needless to say that all of this works fine, when I connect to the same machine using ssh.