on one's honor

Entrusted to behave honorably and honestly without supervision. For example, The students were on their honor not to consult notes during the exam. Originally alluding to a solemn oath, this idiom dates from the mid-1400s.

Words nearby on one's honor

on one's hands, on one's head, on one's heels, on one's high horse, on one's home ground, on one's honor, on one's last legs, on one's mind, on one's own, on one's own account, on one's own time