OK thanks. As you can see, you can measure both resonance and Q at the same time with the shunt resonator method. The null frequency gives the resonant frequency and the depth of the notch can be used to predict the Q. However, the port match of the VNA has to be very close to a true 50 ohms resistive for the notch depth measurement. The source match (port 1) has to be especially close to 50 ohms of errors creep in. The old HP 87xx series of VNAs don't have a very good (uncorrected) source match at low frequencies so it's best to fit something like a known good 15dB attenuator at the end of the port 1 cable and a 10dB attenuator at the end of the port 2 cable if you every try and measure Q based on the depth of the notch. Then do a thru cal to normalise to 0dB and then measure the notch depth.
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If you just want to look for resonance then you don't need to calibrate anything, just do an uncorrected s21 measurement and look for the null frequency at resonance.
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If you want to try making a physically bigger solenoid using thicker wire (to achieve a higher Q) I can help predict the Q using the software program if that helps?