If you have organic contamination on the sample, chemical characterization methods like XPS or EDX will only point to the presence of carbon, and figuring out the exact bonding state of that carbon is non trivial. For the purposes of checking for contamination, you might consider imaging your sample instead. SEM or AFM imaging will reveal any trace contamination on a test area on the sample. I prefer AFM scanning as it can faithfully capture contamination by comparing pre/post processing images. 

How are you cleaning the resists? If you're worried about contamination, consider cleaning your samples with piranha clean. Just make sure if your substrate/material is inert to piranha. Metals like Cr, Ti etc get etched by piranha but oxides and crystalline interfaces typically are inert. 

The easiest and non destructive way to check the remaining photoresist in a very short analysis time is energy dispersive X-ray analyzer (EDX). Which identifies any traces of unremoved photoresist in your chip.

For a quick check during initial optimization of the lithography process, an optical microscope in the dark field can be used as well. It will show the increased surface roughness due to remaining resist. However, for a fine analysis, AFM would be required.

Spectroscopic ellipsometer will do the job.