When you use Firefox or Palemoon or other FFx variants the download of the displayed image will not work. At least for my PM the CTRL+S key to save the image did never work - in stark contrast of what waifu2x.udp.jp itself claims.Single-Image Super-Resolution for Anime-Style Art using Deep Convolutional Neural Networks. And it supports photo.
Therefore I always use the [ Download ] button.
Be patient, it takes a few seconds for the neural network to process your image and thus takes a short while until the "save image as..." window will appear.