WordNet records no synonym and no antonym for redound. It is the only member of each of its synsets, which is common for technical, taxonomic and single-sense vocabulary — there is no other English word that means the same thing. The broader and narrower terms below are the useful relations in that case.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
return or recoil
“Fame redounds to the heroes”
contribute
“Everything redounded to his glory”
have an effect for good or ill
“Her efforts will redound to the general good”
Synonyms, antonyms and the broader and narrower relations for redound come from Princeton University’s WordNet. Full sources and licences.