Measure current draw with high precision (not necessarily accuracy)

Inspired by Nick Gammon's comprehensive writeup on low-power methods (http://www.gammon.com.au/power), I'm now trying to create a barebones Arduino with extremely low-power consumption.

I'm starting with a minimal Atmega328-based setup on stripboard, powered by a Li-ion battery. I want to measure the current draw of the circuit load each time I change something.

QUESTION: What are some methods of measuring the current draw with high PRECISION, ideally with around 1 uA (one microamp) resolution?

I'd prefer to use standard electronics tools: DMM, or oscilloscope, or resistors, etc. But otherwise, pretty flexible on the method since I am measuring draw of entire circuit load (e.g., measured in series with the battery+), as opposed to just a specific part.

I used for the most part a Fluke 87 multimeter, set to the milliamps or microamps range, depending on the test in question. You can set it to high-resolution mode which gives an extra digit of resolution. Dave Jones’ uCurrent device, mentioned in that article, basically confirmed the readings from the Fluke and added a bit more detail on the very low-current measurements.

I understand your desire for high precision, but in the case of saving power, even if the reading is not totally accurate, one presumes that a relative reading would be OK. What I mean is, if one technique says you are using 200 nA and another technique uses 300 nA, even if the 200 and 300 aren’t quite right, you at least know which one uses less power.

To put this into context, if you are running from a Li-Ion battery, which may perhaps have a self-discharge rate of 600 uA, then whether or not your circuit uses 1 uA or 2 uA probably isn’t that relevant, compared to the 600 uA that the battery is, in effect, draining anyway.

@ Nick: Thanks for the clarification!

I read the self-discharge section of your article, but forgot to consider it in context. In fact, the self-discharge might only be greater if you consider the running of the built-it protection circuitry that Li-ions and Lipos have on board when we buy them in the safe form they're usually sold in (e.g., from Sparkfun or Adafruit, etc.).

So in this context I suppose even about 100 microamps of precision should be more than good enough. Although of course for RELATIVE comparison (where the change from one case to another might be on the order of a few microamps), it would be useful to use a high-precision multimeter as you listed. But again, that's not an issue either, because going by your webpage, when a certain power-saving factor is put into place, it is more likely to create a difference/reduction on the order of nearly milliamps (as opposed to one or two microamps).

Measure current draw with high precision (not necessarily accuracy)

Of course, accuracy is important too.

For example, I could claim to be 3.675432 feet tall. Nice and precise. But not accurate, as I am around 6 feet tall.