Depth sensing is a crucial function of unmanned aerial vehicles and autonomous vehicles. Due to the small size and simple structure of monocular cameras, there has been a growing interest in depth estimation from a single RGB image. However, state-of-the-art monocular CNN-based depth estimation methods using fairly complex deep neural networks are too slow for real-time inference on embedded platforms. This paper addresses the problem of real-time depth estimation on embedded systems. We propose two efficient and lightweight encoder-decoder network architectures, RT-MonoDepth and RT-MonoDepth-S, to reduce computational complexity and latency. Our methodologies demonstrate that it is possible to achieve similar accuracy as prior state-of-the-art works on depth estimation at a faster inference speed. Our proposed networks, RT-MonoDepth and RT-MonoDepth-S, runs at 18.4\&30.5 FPS on NVIDIA Jetson Nano and 253.0\&364.1 FPS on NVIDIA Jetson AGX Orin on a single RGB image of resolution 640$\times$192, and achieve relative state-of-the-art accuracy on the KITTI dataset. To the best of the authors' knowledge, this paper achieves the best accuracy and fastest inference speed compared with existing fast monocular depth estimation methods.