Connecting a galvanometer directly to a microcontroller's PWM output
Use a series resistor, scaled such that 100% PWM output (i.e. 3.3V or 5V depending on the MCU) gives 100uA or a bit over (up to 50% over). 

Direct connection would only allow something like 10% duty cycle before full-scale deflection, not very useful. 

And the series resistor will attenuate any inductive spikes from the meter coil well enough to protect the MCU.

It is possible but unlikely that a 2mA overload, e.g. from a software error (integer overflow?) could cause damage to the meter movement. Unlikely to burn the coil out, but it's a fairly violent mechanical movement. 100uA movements should be pretty tough but more sensitive ones used to have delicate jewelled bearings, like watch movements.