While WSPR is often cited as taking the fun out of ham radio, it is perfect for this application. Connect the transmitter and a few hours later, visit a web page and find out where you’ve been heard by an objective observer. If you had a few of these, you could even examine several antennas at similar times and conditions.
The transmitter has its own GPS so it doesn’t require much configuration. You do need to set the frequencies you want to use and — presumably — the SWR at these frequencies of your antenna will be acceptable. Of course, you also need to set your callsign and transmission schedule. You can manually set the location code if you don’t want to get a GPS setting.
Once set up, you don’t need the computer connected. After some time, you can just visit the WSPR.org web site and view who has been able to hear the little low-power transmitter.