Missed the orginal post - but a PIC should onil draw nano amps in sleep mode and ma as required by the circuit otherwise.
The following is a reply to the same problem discussed in another newsgroup. pick a resistor that you believe will drop a tolerable amount of voltage at the average current. For example, if you believe the average current is
150uA, you might pick 1K 1% which will drop 150mV at that current. Then put a capacitor across it to smooth the reading at the repetition rate of whatever pulses etc. are being drawn from the supply. Maybe you pick a time constant of 1 second, so 1000uF electrolytic. This is a single pole LPF. You use the meter in voltage mode, of course. In stubborn cases, you may wish to add a second pole, say a 100K resistor and 10uF tantalum. That won't affect the reading with a >10M input Z, the average current is still 1mV/uA within a couple of percent.
If the voltage turns out to be too large or small - so it drops too much voltage to the circuit, or the voltage is too small to measure easily, then just change it (and the capacitors)
Note that if current is drawn in short pulses you have to make sure that the instantaneous decrease in the voltage is not too high or the reading may be inaccurate or the circuit may malfunction. A 'scope is useful in this regard. You can also calculate it to bracket the problem.
Eg. Supply the 150uA is essentially all composed of pulses: 150mA for
200usec with a 200msec period. A 100uF capacitor would see a voltage change at the terminals of delta-V = I * Ton/C = 300mV, which is a bit high. The
1000uF would yield a more reasonable 30mV, so the troughs would be 180mV down from nominal, not 450mV down. The 30mV/300mV p-p of ripple will yield jumpy readings as the 5Hz frequency "beats" with the measurement cycle of the meter. This is where the second pole filter comes in handy.
Roy