General synonyms:
* Distinguished
* Notable
* Prominent
* Renowned
* Illustrious
* Famous
* Celebrated
* Outstanding
* Exceptional
* Remarkable
* Conspicuous
* Preeminent
* Superior
Synonyms emphasizing high standing or reputation:
* Prestigious
* Reputable
* Esteemed
* Respected
* Honored
* Revered
* Admired
Synonyms emphasizing intellect or achievement:
* Brilliant
* Gifted
* Talented
* Proficient
* Skilled
* Masterful
* Learned
* Wise
Synonyms emphasizing leadership or influence:
* Influential
* Powerful
* Authoritative
* Leading
* Foremost
* Pioneering
The best synonym for "eminent" will depend on the specific context. Consider the specific meaning you want to convey and choose the word that best fits.