How can I check the VHF antenna to make sure it is working?

There are a few options, the easiest is to do a radio check on a commonly used channel for your area (note that the U.S. Coast Guard frowns on radio test calls made to them, Channel 16). Another option is to call a friend on a channel you agree upon from a range of known distances, then have the friend assess your transmission for quality. The final fail-safe option is to measure the efficiency of your antenna/radio system more scientifically. Shakespeare makes an antenna / radio tester – the ART-3 Tester. The ART-3 measures transceiver output power, antenna VSWR, and proper receiver sensitivity.