This would be a cool experiment. Could this be done with the nanovna's?
https://coppermountaintech.com/determining-resonator-q-factor-from-return-loss-measurement-alone/
That article is somehow confusing. They are also using S21 for the calculation..
However, I often use the magnetic field probing for determining the Q factor,
contactless.
There are many applications where the Q factor is critical. For example I use that probing for testing or fine tuning RFID card readers.
The company I am working for are also producing MRI antennas. I can remember we had some problems with some PIN diodes with too high leakage current in some detuning circuits.
It was not possible to measure in circuit, but the additional resistance of that diodes droped the Q factor of the antennas. So we could finaly sort those "bad apples" out, by checking the Q factor.
The probe basically consists of two small magnetig loops, placed in parallel planes, but slightly shifted. The "challange" is to shift and keep them as near as possible one to another, but keep a high decoupling between them. The probe I am showing in the experiment has > 80dB decoupling. It uses RG178, diameter aprox. 20mm and 18mm spacing between the 2 planes. The Another picture is showing some similar H-Probes made of 0.047" rigid cable.
For this kind of measurments I wrote my own software. I am also not a big fan of the graphical method, thats why I used the group delay.
Q = π𝜏f
For this demo I soldered a resonator consisting of a 39pf C and a few uH L, resonating at aprox. 37.6 MHz
Both methods (graphical and gruopdelay) are practically showing same results: Q= 37570/250 = 150 and Q =152
The 2nd method is faster, but is not working well for low Q factors, when the groupdelay is getting "noisy".
Of corse the results also depend on the loading effect..