A tense moment of negotiation requires a firm guarantee of safety. Saul provides this absolute assurance to the woman, swearing by God that she will remain completely unharmed. To secure her trust, he makes a clear and explicit oath using God's name [מצודת דוד]. This solemn promise achieves its goal, and the woman fully believes his words [ביאור שטיינזלץ].
Saul assures her that no bad event will happen to her [מצודת ציון]. The primary approach among commentators is that his promise focuses entirely on the consequences of her actions. Rather than discussing whether the deed itself is a sin, he guarantees that she will face absolutely no punishment for doing what he asks [מצודת ציון, מצודת דוד, ביאור שטיינזלץ].