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on one's honor
Fig. on one's solemn oath; sincerely. On my honor, I'll be there on time. He promised on his honor that he'd pay me back next week.
on your honor
1. without being watched to see if you behave in the right way We ask people, on their honor, to avoid leaving garbage at the campsite.
2. with a serious promise She swore on her honor that she'd finish the assignment.
on (one's) honor
Under an obligation enforced by the personal integrity of the one obliged.