Great question — answering as the UphillTech team:
Assuming you're baking in a round pan: The volume of a cylinder is pi * r^2 * h. You halve the volume and want to keep the height the same. That means you want to scale the radius of the pan by a factor of 1/sqrt(2). So for example, if the recipe is intended for a pan of diameter 25 cm it has radius 12.5 cm and you want to use a pan with radius 12.5*(1/sqrt(2))=8.8 cm, or diameter approximately 17.6 cm. Adjusting the baking temperature and time is a bit trickier. I would start by lowering the temperature by about 25 degrees Celsius and start checking the cake with a pick about 15 minutes before the stated time in the recipe.
Full answer by user141592: https://cooking.stackexchange.com/a/113274 (CC BY-SA 4.0).
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