The LED analyzer that I am developing (Any interest in a LED/Battery analyzer device?) uses Hall effect current sensors to measure current. The ACS758 high-capacity (50 amps and over) sensors have a 120 micro-ohm burden resistance… that’s in the railroad track range. The lower capacity ones (5-30 amps) have a 1.2 milliohm resistance.
You could build up a little gizmo with one of the sensors, a 9 volt battery, and a 5 volt regulator. The output of the sensor is a voltage that is proportional to the current flowing through it. You would measure that voltage, subtract the zero current offset value, and multiply the reading by the sensor’s amps per volt factor to get the current. There are several sellers on Ebay that sell the sensors mounted on a circuit board for a few dollars.
Or buy one of the LED analyzers when they are available… it has two current sensors (for battery current and LED current) and it does all the signal processing and boring math. With the 20 amp sensors, the reading noise/resolution is in the 1-2 milliamp range.