"en" in "examen" ist pronounced /ɛ̃/. Are there examples for "em"?
You got a good answer from jlliagre, who did a great job at tracking the various pronunciations of ‘em’ in French.
I only want to mention a regional (Quebec) way of pronouncing certain words that contain ‘em’, though from all the examples I could find, it appears to include only cases where e comes with an accent, and the pronunciation would be /ɛ̃m/, not /ɛ̃/.
- même /mɛ̃m/
- blême /blɛ̃m/ (but je blêmis /ʒə blɛːmi/, nous blêmissons /nu blɛːmisõ/, etc.)
- problème /pʁɔblɛ̃m/ (but problématique_ /pʁɔblemat͜sɪk/)
- Carême /kaʁɛ̃m/ (but crème /kʁɛm/)
Also interesting, these are true /ɛ̃/ sounds, despite the usual realization /ẽ/ in Quebec of the French phonem /ɛ̃/.