If you have a field strength meter, then you can use that. You can also use a 2nd radio, on a 2nd antenna.
But, consider reciprocity: anything you to do increase your transmit gain also increases your receive gain equally. So actually you don't need a 2nd radio, you can use someone else's.
Simply find a station that's transmitting, tune it in, and measure its strength. With a more efficient antenna, the received power of that station will be greater, and any efficiency gains (or losses) work for transmitting too.
It's easiest if you can find a station transmitting something with more or less constant power, like CW, AM, or most digital modes. SSB is tricky because the transmitted power depends on how loudly the operator is talking. If there's a commercial AM broadcast station handy, that could be a good target.
Getting an accurate measurement is somewhat complicated by the fact that S meters on many radios doesn't mean a thing. Usually the S meter simply indicates the AGC level. How does AGC level correlate to the received power? It's different on every radio, and may or may not be useful.
A cheap SDR like the Softrock or RTL2838 can be useful here. Typically these feed the host computer with data at a fixed RF gain, and then you just need software that can give you a good measurement of power. Most software has some scale on the waterfall or spectrum that will do the job.