The correct answer is character
The fact that Emma is able to trust Natalie is because she is a person of character. This is an important aspect when it comes to trust.
Character is a set of characteristics and traits related to an individual or group's way of acting and reacting. It is a moral character. It is the firmness and consistency of attitudes. The set of qualities and defects of a person is what will determine his conduct and his morality, his character.