Deep learning methods have been very successful at radio frequency fingerprinting tasks, predicting the identity of transmitting devices with high accuracy. We study radio frequency fingerprinting deployments at resource-constrained edge devices. We use structured pruning to jointly train and sparsify neural networks tailored to edge hardware implementations. We compress convolutional layers by a $27.2\times$ factor while incurring a negligible prediction accuracy decrease (less than 1 percent). We demonstrate the efficacy of our approach over multiple edge hardware platforms, including a Samsung Gallaxy S10 phone and a Xilinx-ZCU104 FPGA. Our method yields significant inference speedups, $11.5\times$ on the FPGA and $3\times$ on the smartphone, as well as high efficiency: the FPGA processing time is $17\times$ smaller than in a V100 GPU. To the best of our knowledge, we are the first to explore the possibility of compressing networks for radio frequency fingerprinting; as such, our experiments can be seen as a means of characterizing the informational capacity associated with this specific learning task.