Are crowns tender to bite down on?

Dental Crown: No. You most likely have hyper occlusion (a premature bite). I would highly recommend to go back to your dentist to check and adjust the bite. In some cases, that may also indicate nerve involvement, that will require root canal treatment. Please do not delay and hope it will go a way.

Ideally not but: Newly inserted crowns may be tender to biting pressures. This usually occurs when the bite needs to be further adjusted. It can also occur if the nerve of the tooth is inflamed. Crowns that have been in your mouth awhile and were not previously tender, but become tender, may reflect any one of a number of problems. You should be comfortable and therefore call and have your dentist evaluate it.

Shouldn't be: When properly done on solid tooth, no tenderness should be felt. If tender, see your Dentist to evaluate the bite (occlusion) and test for irreversible pulpitis. May need root canal treatment if pulp (nerve/blood vessels) is irreversibly irritated (imflammation). Good Luck.