Coded aperture cameras can be manufactured cheaply, have a very thin form-factor, and may be transparent and flexible, thus providing easy-to-integrate and compact image sensors. However, limitations in reconstructed image quality and resolution have impeded the growth of their applications. We propose a method to generate high-resolution face images from low-resolution coded aperture sensor snapshots. Using the point spread function of the coded aperture camera, we generate a set of training images to train an image enhancement network. We then apply a face recognition model to extract facial templates and project them into the intermediate latent space of a face generator network to generate high-resolution (i.e., 1024x1024) face images. Our experimental results show significant retention of the subject's identity in the generated high-resolution face images. Our cross-dataset evaluation shows the generalization of our method on other datasets for generating high-resolution face images. To our knowledge, this is the first work for generating high-resolution face images from coded aperture imaging. The source code of our experiments is publicly available to facilitate the reproducibility of our work.