To be uncertain
wonder, question, query, ponder, vacillate, waver, hesitate, be dubious, be undecided, be uncertain, be curious, be puzzled, be doubtful, be in a quandary, demur, hold in doubt, have doubts about, have one's doubts, raise a question, stop to consider, have qualms, have reservations, scruple, call in question, hesitate to accept, hold questionable, greet with skepticism, skepticize, cast doubt upon, have no conception, not know which way to turn, not know what to make of, be of two minds; see also ask 1, question 1.
Antonyms believe, trust*, confide.
To entertain doubt
suspect, mistrust, distrust, lack confidence in, discredit, give no credence to, not believe, refuse to believe, disbelieve, impugn, dispute, be apprehensive of, be skeptical of, scoff, insinuate, misgive, read somewhat differently, challenge, harbor suspicions, not admit, doubt one's word, smell a rat*, not buy*, take a dim view of*, set no store by*, put no stock in*, take no stock in*; see also deny.
Antonyms support*, prove, demonstrate.