There is, of course, the use of an SWR meter with a transmitter to measure the SWR (standing wave ratio) of an antenna at the frequency of interest. Or a dip meter may be used to find the point at which the antenna is resonant.
But a return loss bridge with either a swept frequency generator or noise source and panoramic receiver can give you a graphical reading on the resonant frequency and bandwidth of an antenna with one look.
One way is using a wideband noise source or swept signal source, a directional coupler or return loss bridge, and a panoramic receiver (ie, spectrum analyzer) like an RTL-SDR.
50kHz to 1.5GHz return loss bridge:http://www.wetterlin.org/sam/SA/Operation/Bridge_BalunPlusBeads.pdf
Three bead balun return loss bridge, 250kHz to 1.5GHz with 3dB pads on the input and return loss output:http://www.wetterlin.org/sam/SA/Operation/3BeadBalunBridge.pdf
How it works: A return loss bridge sits between the wideband noise source and the antenna. With no load or a short, all of the signal is reflected back. That is your reference level from the return loss bridge. The better a match the antenna is, the more of the noise signal is radiated at that frequency, and so less of the noise is bounced back. This gives you a measure in dB between the fully reflected signal and the reflected signal at any particular frequency, which can be converted to SWR with a chart or lookup table.
A video that explains it pretty well:https://youtu.be/EDbS-zlLPxw?list=PL1295F604A4A2D331
A page that goes along with the video:https://drive.google.com/file/d/0B7Bk3JifFLbSbTVNUWduLU9lR2s/view
A good return loss bridge is easier to homebrew than a good directional coupler. If you aren't trying to get insane bandwidth, a ferrite core with bifilar windings and three 1% 50 ohm resistors (or six 100 ohm 1%) can give you very good isolation. Use metal film or carbon composition resistors as they have flatter frequency characteristics. You will lose 6dB of signal, but even so, 10mW is generally enough to drive it.http://www.qsl.net/kl7jef/Build%20a%20Return%20Loss%20Bridge.pdf
That one is $20 from Aliexpress. Although it can be better if you put a 3dB pad at the input and at the reflection output to isolate any impedance mismatch problems from those ports, it does require more power at the input.
Of course, you can have a few return loss bridges for different frequency ranges. It'd be nice to be able to tune 2.4GHz WiFi antennas, for instance.
Here is one that goes up to 3.5GHz using two sections of RG174 coax in ferrite beads, one "turn":http://www.studioadriana.com/vk5fe/?page_id=684
Lots more interesting construction articles there.