Q:

Ways to measure current in picoamperes

I need to check the low power consumption of a microcontroller in the range of picoamperes.  I only have a multimeter capable of measuring milliamperes and as such it shows 0. 
Is there an easy and precise way to measure picoamperes? 

A:

Power the micro-controller with a capacitor, charged to a known voltage.  Wait an appropriate amount of time, then measure the voltage.  Calculate the current from the delta-V and the C. (Don't measure the voltage continuously, unless you have a meter with a high-enough impedance, because that might draw extra current.)  You will need a capacitor with known capacitance, but in a pinch you could measure a capcitor in the same way by discharging it through a known resistor. 
As the comments point out, other current paths might contribute to the discharge of the capacitor (including self-discharge).  You could repeat the measurement with the UC removed and see what value that gives.  Then you might think about whether you can realisticly avoid such 'other' currents in your design. 
And don't forget your batteries self-discharge and/or ageing! 
If you aim is too 'see' the power-down mode of the chip in action you could use the capacitor, build a simple circuit that periodically connects it to the power supply (if possible synchronysed with the uC's activity cycle, must have a realy low leakage current!),  and watch the C's voltage on a scope (the scope impedance must be higher than the UC's current consumption, or you might even use AC coupling if the uC"s activity cycle is short enough).  This way you can verify both the time-wise division in high and low current consumption, and the currents in both modes. 

A:

One simple method I've used is to put a resistor in series with the power to the micro and parallel it with a capacitor.  The leakage of the capacitor is not as important in this case.  
For example, if you think the supply current should be no more than 10nA then you can use a resistor of value 10M 1% in parallel with a 1uF ceramic capacitor.  That will give you 100.0mV for 10nA (so the burden of the ammeter is 0.1V, which should not overly affect the circuit- raise the input voltage up a bit to compensate for the drop if it bothers you).  
Then look at the voltage across the 10M resistor using a voltmeter with high input impedance, such as the Agilent 34401 in >10G input resistance mode.  The bias current of the meter will influence the reading, but it is less than 30pA (0.3%) at room temperature.  
The 10M/1uF combination filters out spikes unless they are happening at very low frequency (if, for example, your processor wakes up once every 10 seconds and draws 0.5mA for 100usec it won't work very well).  

A:

The power or current consumption of a microcontroller can be very irregular depending on the µC's state.  For example: 1pA for 999 ms and then 1uA for 1 ms.  On average that would be 1.001 nA. If your multimeter would do a measurement every 100ms, it would never measure the 1.001 nA ! 
In this case you need to use a resistor in series with the supply and an oscilloscope to measure the voltage across the resistor to "see" the actual current over time.