conjecture has 13 distinct synonyms spread across 3 of its 4 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.
a hypothesis that has been formed by speculating or conjecturing (usually with little hard evidence)
“speculations about the outcome of the election”
a message expressing an opinion based on incomplete evidence
reasoning that involves the formation of conclusions from incomplete evidence
to believe especially on uncertain or tentative grounds
“Scientists supposed that large dinosaurs lived in swamps”
Synonyms, antonyms and the broader and narrower relations for conjecture come from Princeton University’s WordNet. Full sources and licences.