Would your advice be any different if the microphones in question (M49, U67) had not been powered up in a few years? It's a very long story....
Electrolytic capacitors, mainly used in the PSU, need to “reformat” for full capacity after a long idle period.
This happens when they are powered with their normal use voltage again and may take a little time.
No extra measures need to be taken to do this.
You probably won’t even notice the effect, as the PSU filters have a significant margin for doing their work.
Another case are possibly broken / dried out caps, they stopped working and will not come back.
You will notice hum in the audio if this is the case.
Not very likely, as the big old caps are much better in this regard than modern small ones.
I’d make sure the mic’s and PSUs are free from humidity they may have collected over the time.
I had such cases here.
Warm them up slightly above room temperature (exact value doesn’t matter, don’t fry them) for some hours, then power them up the normal way.
