There are several synonyms for the phrase "his eminence." Some of the most commonly used include "excellency," "distinguished," "elevated," "noble," and "prestigious." Each of these terms carries a similar connotation of high status and importance, and is often used to refer to respected leaders in various fields such as politics, religion, or academia. Other synonyms might include "lordship," "highness," or "majesty," though these are usually reserved for royalty or other extremely high-ranking figures. Regardless of which synonym is chosen, using these terms is a great way to show respect and admiration for those who have achieved greatness in their respective areas of expertise.