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.
(..) Together, you have the might and power... ...to retake Erebor. Summon a meeting of the seven Dwarf families. Demand they stand by their oath. The seven armies swore that oath to the one who wields the King's Jewel. The Arkenstone. It is the only thing that will... ...unite them, (..)2013 The Hobbit: The Desolation of Smaug