capacitor - Reading very low capacitances with Arduino

I'm trying to measure the capacitance of a very low capacitance sensor (two parallel plates across a block of foam). This is a self-produced force sensor; I'm trying to eventually use some of the work presented here. I'm estimating that the capacitance should be in the neighborhood of 90 pF.

I started with the CapacitanceMeter tutorial from the Arduino web site. I modified it to use micros() instead of millis() and output pF instead of nF. I also swapped in a 10 megohm resistor in place of the 10K ohm one, and updated the code. However, I'm getting readings that swing by over 50 pF.

How can I improve the accuracy of the setup?

Thanks!