Your needs can be met by mobile phone apps such as Shredder. Dedicated mobile chess computers are not in production anymore. The last one made with the feature to watch the candidate moves was the Mephisto/Saitek Micro Travel chess computer.
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This is perhaps a slightly different twist than the threads I'm seeing around this topic. I do not want a chess computer that comes with its own pieces. I don't want to have a board in front of me while I insert moves that Fritz is making on my desktop. I'd love something that looks like a King Upgrade Module (wander over to House of Staunton if you want a picture), where I can input whether I want to play white or black, time controls, etc. and then just have a tiny window that shows my inputted move and the computer's response. I don't think it's actually that odd that I'd like to get to play chess using one of the numerous collectable sets I have boxed up, on one of my boards, is it? Surely someone has thought about this and produced a commercially available product (?)