How can I test a COM VHF antenna?
Your radio shop may be able to test the SWR of the antenna working with the COM radio.  That would be my starting point.  However, sometimes problems like these are intermittent and difficult to isolate.

You can test the antenna with an ohm meter but that will not measure the impedance at transmit frequencies.  An SWR meter will.  

Unfortunately, unless your other hobby is ham radio, you may not have the equipment on hand to check out transmitter operation.  But your radio shop will.

They will also have a dummy load for testing the transmitter.

I have to say that I am surprised that the unit blew a fuse.  Most aviation radios I have experience with (I am not an avionics tech only a ham) have protection against shorts or opens on the output of the transmitter, which usually shut down the power of the transmitter, for example when a high reflected signal comes back. So blowing fuses is normally extremely rare.