perambulate has 2 distinct synonyms spread across 1 of its 2 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.
make an official inspection on foot of (the bounds of a property)
“Selectmen are required by law to perambulate the bounds every five years”
walk with no particular goal
“we were walking around in the garden”
Synonyms, antonyms and the broader and narrower relations for perambulate come from Princeton University’s WordNet. Full sources and licences.