Deep learning–based speech recognition applications have made great strides in the past decade. Deep learning–based systems have evolved to achieve higher accuracy while using simpler end-to-end architectures, compared to their predecessor hybrid architectures. Most of these state-of-the-art systems run on backend servers with large amounts of memory and CPU/GPU resources. The major disadvantage of server-based speech recognition is the lack of privacy and security for user speech data. Additionally, because of network dependency, this server-based architecture cannot always be reliable, performant and available. Nevertheless, offline speech recognition on client devices overcomes these issues. However, resource constraints on smaller edge devices may pose challenges for achieving state-of-the-art speech recognition results. In this paper, we evaluate the performance and efficiency of transformer-based speech recognition systems on edge devices. We evaluate inference performance on two popular edge devices, Raspberry Pi and Nvidia Jetson Nano, running on CPU and GPU, respectively. We conclude that with PyTorch mobile optimization and quantization, the models can achieve real-time inference on the Raspberry Pi CPU with a small degradation to word error rate. On the Jetson Nano GPU, the inference latency is three to five times better, compared to Raspberry Pi. The word error rate on the edge is still higher, but it is not too far behind, compared to that on the server inference.