Coaster for glassware - the underside/base is a solid ridge near the edge for stability. Typically the face-up side has short straight sides to contain the condensation. Try looking for Kaiser coasters. They typically came in sets of 6 or 8 (depending on the subject) and were very popular in the mid 1900's.
They also made sets of "butter pat plates" that are smaller, but people will mistake the coasters for them. Butter pat plates are smaller and the underside/base ridge is towards the center of the piece (which would tip if a glass was small enough to fit in them). Typically the face-up side has sides that gracefully curve upwards (allows for easy access with a butter knife).
