get an SPL meter and use that.
Without it, there's ways to get it close. You have to keep a few things in mind.
1. the headphones have impedance (or resistance). This means that the current capacity of the amp is now a factor (if you're maxing the current capacity, it'll not be able to deliver full voltage to the HP and it'll be quieter. It'll also sound like garbage)
So either plug in the headphones, and then set volumes so the voltage is the same. I suggest 1 KHz tone since most headphones are normalized in their frequency response graph at that point (it's a convenient tone to use for standardization).
Alternatively, get a resistor that's similar to the headphones and run your 1 KHz test track through that.
Note: if one is a transconductance amplifier (
transimpedance amplifier) (plays games with current) this might not work.
That's a good idea with the multimeter. I think it'll work out.
Then of course sanity check by listening to both before the start of the test.
---
Please correct me if I'm wrong. I don't have a degree, so from a social perspective I have no authority to speak here.