Claim: Established in 1893, the Principality of Trinidad was an unrecognized state that has a self-proclaimed monarchy.
Evidence: The Principality of Trinidad was a short-lived unrecognized state declared in 1893 when the American James Harden-Hickey claimed the uninhabited Trindade Island in the South Atlantic. Self-proclaimed monarchy 
1893 Self-proclaimed monarchy Unrecognized state