This paper describes computational processes which can simulate how human designers sketch and then iteratively refine their work. The paper uses the concept of a map sketch as an initial, low-resolution and low-fidelity prototype of a game level, and suggests how such map sketches can be refined computationally. Different case studies with map sketches of different genres showcase how refinement can be achieved via increasing the resolution of the game level, increasing the fidelity of the function which evaluates it, or a combination of the two. While these case studies use genetic algorithms to automatically generate levels at different degrees of refinement, the general method described in this paper can be used with most procedural generation methods, as well as for AI-assisted design alongside a human creator.