Magnetic and electromagnetic induction (EMI) surveys are the primary techniques used for unexploded ordnance (UXO) remediation projects. Magnetometry is a valuable geophysical tool for UXO detection because of the ease of data acquisition and its ability to detect relatively deep targets. However, magnetic data can have large false alarm rates caused by geological noise, and there is an inherent non-uniqueness when trying to determine the orientation, size and shape of a target. EMI surveys, on the other hand, are relatively immune to geologic noise and are more diagnostic for target shape and size but have a reduced depth of investigation. We aim to improve discrimination ability by developing an interpretation method that takes advantage of the strengths of both techniques. We consider cooperative inversion, where information from the inversion of one type of data is used as a constraint for inverting another. We compare the confidence with which we can discriminate UXO from non-UXO targets when inverting the data sets cooperatively, to results from individual inversions. Examples are given of the application of the methodology to time domain electromagnetic induction (TEM) and magnetic data sets collected at the Yuma Proving Ground UXO Standardized Test Site calibration grid and the Former Camp Sibert.