A married woman needed her husband's approval to make vows and pledges. Her husband could cancel her religious promise. But he had to decide on the day he heard about it. God did not blame the married woman for breaking the promise if her husband canceled it correctly (compare 30:5, 8, 12).
The self-denial mentioned in 30:13 probably refers to fasting. If he did not object, the husband's silence meant he agreed. He could not delay his objection, or he would be guilty of a broken vow (compare Leviticus 5:4–13).