Actually, it's quite possible to run NMR on paramagnetic compounds. My grad project was making organometallic iron compounds....as you might guess, relatively few of them were diamagnetic.
(this mostly concerns 1H NMR)
Step 1. Lower your expectations ... you most likely will not see splitting patterns, instead integration and a bit of educated guesswork will be your friends. Understand the more unpaired elections, the worse your resolution. You can still guess at basic symmetry: 'how many peaks do I have?' if not actual environment.
Step 2. Expect a !large! ppm window. Mine was usually -30 ppm - 80 ppm for all my peaks. If you have NMR specialists running the machines, bring them a cup of a coffee and ask them nicely to help you find the right settings on your system to shim it properly with that large of a window.
Step 3. Scan a book on NMR ... most graduate level ones will discuss the paramagnetic effect's influence on t1 and t2. If you want I can dig out mine to recommend, but again, who's ever in charge of the NMR can help you out better. Next, find and read about this topic:
Evans Method ( of determining magnetic susceptibility in liquids ) -http://www.measurement.sk/2005/S3/DeBuysser.pdf
- will get you started ( be sure to check out the JChemEd paper, dead simple example). It's a large amount of high-school math, but once you get the hang of it, you can get your mu-b in a few minutes.
Happy to answer further questions, if I can remember the answers.