on oath
Bound by a formal promise to tell the complete and honest truth about an event while on the witness stand in a trial. You are on oath as a witness in this trial, so you must answer my questions completely truthfully! Consider your answer carefully—you're still on oath.
on/under ˈoath
(law) having made a formal promise to tell the truth in a court of law: Is she prepared to give evidence on oath?The judge reminded the witness that he was still under oath.