Charge the capacitor to 5 volts. Then, with a timer, measure how long does it take to discharge the capacitor to 1.85 volts (37% of the initial value). If you discharge the capacitor through a constant resistor (conected across the capacitor), then the capacitance is C = T/R. I believe you can use the PIC comparator to stop a timer when the voltage drops below the 1.85 volts. The equation comes from the time constant T = C*R, which tells how long does the rc-circuit take to reach 63% of a step function.
If you discharge the capacitor with constant current, then the capacitance is C = (I*T) / (5V-1.85V). In this method, you can choose the initial voltage and the discharge voltage more freely, but you need a good constant current circuit to discharge the capacitor.