How about using a resistance box and a fixed DC voltage supply?

Put the resistance box in series with the meter and DC supply.
Adjust resistance box (R1) to give ½ full scale deflection.
Adjust resistance box (R2) to give full scale deflection.

Rmeter = R1 - 2R2

 

If you'd like the harder way, take a variable series resistance in series with a meter and a voltage source. Adjust the voltage across the meter so it equals the voltage across the resistor, then the the meter resistance and the resistor have the same value. measure the variable resistance and you have the meter resistance.

Using 1/2 scale make sit come out in the wash.

I did not cover turning the ammeter into a voltmeter or extended scale ammeter, but the meter resistance needs to be known.

The test current has to be within the range of the meter (1/2 scale or more works nicely). this can be achieved with a variable DC supply and a variable resistor.