To say that what you have said is surely true; promise seriously that it is true. Often used by children in the longer form. Children often make a sign of a cross over the heart as they say it, for emphasis.
Поклясться; "не сойти мне с этого места"; "вот тебе крест".
"Cross my heart, I didn't hide your bicycle," Harry told Tom.
"I didn't tell the teacher what you said. Cross my heart and hope to die," Mary said to Lucy.
I can swear that everything I say is true. Cross my heart and hope to die.
Я могу поклясться, что все, что я говорю, правда. Не сойти мне с этого места.