Neuromorphic computing represents one technology likely to be incorporated into future supercomputers. In this work, we present initial results on a potential neuromorphic co-processor, including a preliminary device design that includes memristors, estimates on energy usage for the co-processor, and performance of an on-line learning mechanism. We also present a high-level co-processor simulator used to estimate the performance of the neuromorphic co-processor on real applications. We discuss future use-cases of a potential neuromorphic co-processor in the supercomputing environment, including as an accelerator for supervised learning and for unsupervised, on-line learning tasks. Finally, we discuss plans for future work.