promise has 8 distinct synonyms spread across 3 of its 6 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
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.
promise to undertake or give
“I promise you my best effort”
make a prediction about; tell in advance
“Call the outcome of an election”
give grounds for expectations
“The new results were promising”
a verbal commitment by one person to another agreeing to do (or not to do) something in the future
grounds for feeling hopeful about the future
“there is little or no promise that he will recover”
Synonyms, antonyms and the broader and narrower relations for promise come from Princeton University’s WordNet. Full sources and licences.