on honor

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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.
See also: honor, on

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.
See also: honor, on

on (one's) honor

Under an obligation enforced by the personal integrity of the one obliged.
See also: honor, on