How to measure headphone impedance for a target cut off frequency?
Relying on the headphone impedance for filtering is probably a bad idea. Different kinds of headphones will be significantly different. Even different instances of the same model of headphones can be different. The headphone impedance isn't just resistive but also reactive, and it will take some work to characterize it. Someone might plug your thing into a line input, instead of headphones, and expect it to work.

Instead, consider buffering the output. For headphones, an op-amp will do. You can, in fact, find tons of designs online for "headphone amplifiers". Some of them even use very expensive op-amps from Burr-Brown costing $50 or more, and, I'm told, these sound better than unobtanium flux linkages. Personally, I just use whatever op-amps I have in the parts drawer. Anyway:







simulate this circuit &ndash; Schematic created using CircuitLab

Now calculating C1 is easy, because you also get to pick R1. Just make it anything significantly bigger than your source impedance. Make C1 whatever you like to get the desired frequency response. The headphone impedance is largely irrelevant, because the output impedance of OA1 is so small.