@MarcT you need two things to make such low resistance measurements.
You need a specialized measurement setup that allows for the lead resistance to
not factor into the resistance measurement. The leads on a 2-wire Ohmmeter will be much higher resistance than the device you are testing, in this case a little piece of copper with very low resistance. Please read chapter 3.3.1 of the Low Level Measurement Handbook:
You also need a ammeter that supports four-wire measurements and can measure on the order of tens of uA, like the example
@Speedskater gave.
Actually, you need two other things:
A solid background in measurements since you are starting out with a difficult measurement that you don't seem to fully understand.
A reason to do this measurement. Transport in metals is a studied subject... think of Ohm, Kirchhoff, Sommerfeld, Drude, et. al. The actual conductivities of metals has been studied, and tabulated across temperature. The calculation that
@antcollinet provided is really accurate, and you are not likely to push the boundaries of physics with a fancy ammeter. And none of this is relevant to audio, you could use steel nails as jumpers and
not affect the response of your speakers in an audible fashion.