I use this technique smooth out all the bumps when measuring battery powered devices which go In & Out of sleep with HUGE current spikes while drawing in the ua range for most of the time, like pulsing a high current LED once every 2 seconds...
Send power to a first main cap, a series precision 10 ohm resistor on the + between that cap and the + of a second equivalent cap which then powers your device. All the - should be connected to GND.
Now, on the power source side of the 10 ohm resistor, place a 1k resistor to a 1000uf cap + and the - of that cap to the other side of the 10 ohm resistor.
Now, place your meter on mv and measure the voltage the 1000uf cap.
Every 10mv = 1ma. If the reading is still too inconsistent raise the 1000uf.
If the reading takes way to long to settle at a particular reading, shrink the 1000uf cap.
Changing the precision 10 ohm to 100ohm means 100mv = 1ma.
(Hope I got my decimal places correct...)
Adding additional series resistors between the PSU and first cap, like 10 or 100 ohm, will also smooth things out even more as well as using something like 470000uf caps as the first and second cap.