To answer your question, the serious method is using a network analyzer like this one: http://sdr-kits.net/VNWA3_Description.html
Of course there are also commercial ones at much higher cost.
However, you could use a regular SWR meter for 2 m and 70 cm and check out the values your antennas produce. This is a much cheaper way but also not as accurate.
I know that the Baofeng UV-5R stock antenna is so bad, it gets warm after just some minutes of transmitting. That clearly is a sign of a terribly bad antenna.