Determining changing values of C in RC circuit
I don't know what kind of accuracy you're looking for, but the capacitor in that circuit will charge up to 140mVDC.  When the capacitance changes, the charge on the cap will not change instantly, so the DC voltage will change by an amount proportional to the change in capacitance (reduced when the capacitance increases).  Of course, it will immediately begin to charge up to the 140mV value based on the new value of capacitance.  An external resistor much larger than the one in the model will help you measure that change from outside the black box.

In order to get a reference measure, though, amplitude and phase should work.  Remember that the voltage across the resistor is in phase with the current, and the voltage across the cap is 90 degrees out of phase with the current.  The vector sum of those two voltages (eliminating the 140mVDC) is the applied voltage.  From there you can determine both values.