The term 'Cross My Heart, E.g.' is an expression of sincerity and commitment. It is often used when making a promise or expressing a strong belief. The crossword solutions for this term are VOW (3 letters) and AVER (4 letters). A VOW is a solemn promise or pledge, usually made to God or a saint, and is often associated with religious ceremonies. An AVER is a formal declaration or assertion, typically made in a court of law.