This video explores the effect of DC Bias on Class II MLCC Capacitors and why once you’ve deployed a ceramic capacitor in your circuit, the capacitance may not be the same as the specified value.
Above is the schematic for the test PCB. The parts listed are only suggestions and not particularly critical. You may want to select a Zero-drift chopper stabilised op-amp for U2 to give the best results. (I used LM7321 for U1 and AD8628ARTZ for U2).
The PCB should be powered from 5V, and once you have a capacitor soldered down, adjust RV1 so that the output is at 1V precisely. As you apply a bias voltage at J1, you will see the effect of bias voltage on the capacitor.
Since the output is calibrated at the start of the test to 1V and the output is proportional to capacitance, you can simply multiply the nominal capacitor value by the output voltage to work out what the actual capacitance is at your test voltage.