Measuring GameBoy power consumption
I had the same problem, with a battery powered Arduino circuit. It would wake up for a millisecond, every second, to check for input and then sleep. I wanted it to last a long time on a battery. With only a multimeter, how do you measure the power consumption?

I got good accurate results by powering the circuit from a large capacitor (to ground), and a carefully chosen resistor (in series with the power supply. This "smoothes out" the current consumption, making it possible to measure with a multimeter.







simulate this circuit &ndash; Schematic created using CircuitLab

R1 is chosen to have a reasonable voltage drop at the average current. C1 is chosen to keep the time constant of the RC a few seconds or longer, so you can read the multimeter.

For example, if you expect your processor to use 100 mA, 5% of the time, the average current is 5 mA. A 220 Ohm resistor will drop about 1 V at 5 mA, which should be ok. (if it's battery powered, that's just the differ between full and empty batteries).
Now choose a capacitor such that R*C > 10 s, so the variation in 1 second will be under 10% . In this example you'll need about 47 000 uF. This size is not difficult to find; get some bigger ones while you're shopping.

Things to watch out for:  


when the processor is in full-speed mode for more than a short time, it will quickly drain the capacitor, and the 220 Ohm resistor won't be enough to supply the current. To stop this from resetting your circuit, keep the resistor short-circuited with a jumper or Croc-lead, until your circuit has booted up and is in power-save mode.  
the current reading will change slowly, so you need to wait a while for it to settle.
voltage variations from the power supply side will cause current variations too, so rather use a regulated supply than a battery.
you must pre-charge the capacitor before connecting your circuit, otherwise the slow rise in voltage could cause it not to start up properly
all of the above ideas depend on your circuit having some sort of voltage regulator in it, so it can accept variable voltage and still work well. If it's strictly 5 V in, then you might need to add your own regulator, and supply it with 9 V from the RC arrangement. The current reading will still be accurate (if it's a linear regulator).
capacitor leakage, and other leaks like a voltmeter, if you are using the above circuit to measure microAmps. Test with and without the circuit in question