Hi,
To measure low resistance values often a bridge circuit is used where the ratio of two resistors allows you to calculate the lower value resistor.
But there is another way too. We are lucky here in that we can use DC current to measure resistance. That means we can use low bandwidth op amps that have very very low input offset. Using this op amp we can amplify the voltage across the voltage across the resistor ten or even 100 times, and this helps relieve the current requirement needed to measure low ohm values.
For example, for 10mOhms at 10 amps would produce 0.1 volts, which could easily be measured down to 1 mv, but 10 amps is still a little extreme. Using 1 amp we would only see 10mv, but amplifying this 10 times we're back up to 0.1 volts which again we can easily measure.
The trick is to pick an op amp with an auto adjusting input offset voltage. These are typically the chopper stabilized op amp types. You set the op amp up for a gain of 10 and you then calculate everything based on that.
If you want to shoot for a gain of 100 you could do that i guess. That would give you more output voltage vs what was actually being measured.
So for a reasonably simple circuit you could measure 10mOhms and get a reading of 0.100 volts, where 0.101 volts would mean 10.1mOhm..
A few things you have to be careful about are:
1. Not overheating the part being measured, even with 1 amp.
2. Taking the lead resistances into account, possibly by shorting them first and doing a 'tare' measurement first, then subtracting that from the final measurement.
3. Making sure the 1 amp (or whatever) current source is accurate, which means you'd have to calibrate.