Definition
When someone is on their honour to do something, it means they are being trusted to fulfill a promise.
以名譽作保證
I am on my honour to keep this secret.
我以名譽擔保會保守這個秘密。
He was on his honour to finish the project on time.
他以名譽擔保會準時完成這個專案。
She was on her honour to return the borrowed book.
她以名譽擔保會歸還借來的書。