I think the best method for measuring loaded and unloaded Q and at the same time the coupling factor
is by using the resonance circle that is created on the smith chart of VNA. Read the article by late Darko Kajfez from Miss State Univ (olemiss)
it becomes a bit tricky for very high unloaded Q or very weak couplings but still usable and I had seen several imporvements
on that method but i cannot remember where...I have only used his method with a simple computer program that I wrote
to analyze the S11 collected from the VNA
