Measuring output impedance
You really need one of a number of options, none of them are hobby friendly if you are above a few MHz. I would guess you are at 2.4GHz, or at 900MHz.

Professional Options

If you might know someone whom has access to equipment that would help you have a few options.


VNA- Vector Network Analyzer. This can give you a smith chart over a frequency range and make sure it shows you at 50 ohms. You can also measure S11 which should be less than -20dB
Spectrum Analyzer- This should allow you to determine your power received at your frequency. This is not ideal, but it should get more output power as you get closer to a proper match.
SWR Meter-As Is noted in another answer and I always forget about, you can use an Standing Wave Ratio meter, but I would still suggest a VNA. They have significantly more features, and can do anything a spectrum analyzer or SWR meter can do.


 Hacker style ways to approach it

There is another funny way to approach this, the problem being you will need to build one of a few microwave components.

You could use an isolator and measure its temperature, hotter isolator is equivalent to a worse mismatch. this is not even close to good method as at 10dBm it will be very hard to detect a temperature failure.

You could build your own mixer and feedback your output signal and mix it with your signal returning from the connection. To take away your signal from the feedback you need to use what is called a circulator. This is not fun, but it is doable.

If you would like to try either method, which is similar to creating your own VNA, I can get you more information on how to build these devices.