They 'swore' (an oath of) allegiance to the United States of America. [=they formally promised that they would be loyal to the United States of America]
He 'swore us to secrecy/silence'. [=he made us promise not to tell anyone his secret]
He was so disgusted by the election results that he 'swore off' politics for good.
(..) and a split second later heard a body hit the floor. - One second later. - Right. Second: The woman across the street swore positively she looked out of the window and saw the killing through the last two cars of a passing el train-the last two cars. - What are you givin' us here? (..)1957 12 Angry Men
(..) into his father. The time is . on the nose. Everything fits. She's known the kid all his life. His window is opposite hers across the el tracks. She swore she saw him do it. Through the windows of a passing el train. This el train had no passengers on it. It was just being moved downtown. (..)1957 12 Angry Men