There are records of tesserae being used during war to allow military leave. There are also examples of voting tesserae, which were given out to Roman citizens to allow them to vote once in a Roman election, then snapped so they could not be reused.
Tesserae were also widely used as admission tickets, invitations to events, or meal vouchers. One of the most well-preserved examples of a wooden tessera is called the tessera nummularia (“coin token”), which entitled the bearer to a dole of grain.