Excitation levels in terms of mechanical oscillation are WAAAAY different for resonance and antiresonance frequencies as driven by a low signal impedance analyzer. Resonance excitation can be 10 to 1000 times higher for the same voltage settings.

In piezoelectric devices, excitation levels make a huge difference on performance, so the antiresonance measurements are sorta wrong and cannot theoretically be used with the resonance frequency for calculations. If we assume the excitation level is so small, we don't have to worry about this. Did I ever mention that assumptions are the fodder for inconclusive results?

The take away message is this: if your resonance and antiresonance frequencies have an impedance difference of more than 5x, you should strongly consider using equivalent circuit analysis using only resonance frequency analysis to determine the coupling factor.

Please hit reply if you need more clarification on this!