There are lots of ways. One way I like is to insert a phase shifter between the reference ocillator and the PLL chip.
You apply a few degrees of phase modulation with the varactor diode to the reference. Since the PLL is "phase locked", it will make the oscillator track that phase modulation when the frequency of the phase modulation is within the loop bandwidth. When the microwave VCO stops tracking that modulation, you are beyond the loop bandwidth.
So you set up an external lab generator set to maybe 1 KHz and attach it to the varactor. You look on your spectrum analyzer and see two sidebands, +/- 1 KHz from the carrier. You adjust the external lab generator so that the two sidebands are easily seen, maybe 30 dB down. then you leave the level fixed, but vary the frequency higher. the sideband level in dBc down will stay fixed until you get near the loop bandwidth.
At that point, if you have a well damped loop, the spur level will be 3 dB lower than the other values, and at that exact Fm frequency, you know your loop bandwidth. If, on the other hand, you have a poorly damped loop, or maybe even an unstable loop, the sidebands might actually peak up 6 or more dB at the loop bandwidth frequency before heading down again. That tells you to play around with your loop filter parameters, especially your zero frequency, until the peaking mostly goes away.
Rich