on one's honour BrE
on one's honor AmE

"Have you never taken a man on his honor before?"

On your honor, you will not take or offer service elsewhere in that time without our leave.

Oh yes, they were keeping that dark, but he was sure of it, on his honor!

A festival, a college and a club were named on his honor.

That he was a man who stood on his honor and loyalty?

However, there has been made a monument in front of the school on his honor.

"We will have to rely on the employees' honor and their common sense."

And she'd promised, on her honor, that she would not get into trouble.

"And on your honor, you have no cause of hatred against me?"

"But I am not willing to chance my brother's life on a woman's honor."