Isolating the USB port from the laptop eliminated a nasty ground loop, turning off the OLED while making measurements stifled a huge noise source, and averaging a few ADC readings produced this pleasing plot:

Those nice smooth curves suggest the tester isn’t just measuring random junk.
The OLED summarizes the results after the test sequence:

Collecting all the numbers for that resonator in one place:
- C0 = 1.0 pF
- Rm = 9.0 kΩ
- fs = 59996.10 Hz
- fc = 59997.79 Hz
- fc – fs = 1.69 Hz
- Cx = 24 pF
Turning the crank:

I ripped that nice layout directly from my November Circuit Cellar column, because I’m absolutely not even going to try to recreate those equations here.
Another two dozen resonators to go …
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