Redounding to the honor of someone or something implies that their reputation has been enhanced or elevated. There are several synonyms for this phrase that can express a similar sentiment. Words like "enhance," "boost," "augment," "uplift," "improve," and "elevate" may be used to indicate that an action or event has led to an improved reputation or better standing. Additionally, words such as "impress," "inspire," and "command respect" may be used to convey the idea that someone or something has gained recognition and admiration as a result of their excellence. Synonyms like these can be useful in alternate contexts where the phrase "redound to the honor of" may not be appropriate.