How do you measure an output designed for a moving coil meter, using an Arduino?
Ideally with isolation from the radio.   


It is easier to measure the meter voltage.   

The following circuit doesn't give true isolation between the radio and your Arduino circuit. However if the radio electronics is isolated from the mains the circuit could work well. You will have 100K ohms separating the radio from the Arduino.  Also, the op-amp circuit won't load down the meter (well, 200K isn't much load across meter, but will have an effect). 

The amplifier shown has gain of -1.  Connect V4 to the positive of your meter and V3 to the minus of your meter.  Diode D1 is to prevent negative voltage from reaching your Arduino.  Check the Vout for proper operation before connecting to your Arduino.  

You can also put a capacitor across D1 to smooth out the signal, or use averaging in the Arduino program. 

The +Vcc (V1) to be 5 volts so the Arduino won't ever experience an over voltage from V1. The Op-amp is close to rail to rail, but output voltage can only go to 4.9 volts (and dependent upon what op-amp you choose).