The answer(s) to your question depends on what you want to know about it and what type of Tuner it is.
For example, I have a homemade manual Tuner that I built many years ago, and, having learned a lot more about impedance by now, wanted to know what the characteristics of the Tuner were as far as impedance and the effect that it has when in line and in bypass. I calibrated the vna to the end of my patch cable to a 50 ohm dummy load over 2-30 MHz, then connected the load to the output of the Tuner and the cable to the input of the Tuner. It was pretty bad.... both in line and bypass. I cleaned up the wiring and improved it, although it is still not ideal.
The other way I use the vna with the Tuner is to find and record the settings for a range of frequencies in each band. For that, I use both channels displaying swr, logmag, phase and the Smith Chart. By observing the changes in the Smith Chart, I can dial in the settings for the desired frequency and tweak the response around it.. I like to try to get the logmag down to -40 dB at that frequency if I can, but that is only at the exact frequency.