HMS Amethyst was a modified Black Swan-class sloop of the Royal Navy. She was laid down by Alexander Stephen and Sons of Linthouse, Govan, Scotland on 25 March 1942, launched on 7 May 1943 and commissioned on 2 November 1943, with the pennant number U16. After the Second World War she was modified and redesignated as a frigate, and renumbered F116.

The Black Swan class and Modified Black Swan class were two classes of sloop of the Royal Navy and Royal Indian Navy. Twelve Black Swans were launched between 1939 and 1943, including four for the Royal Indian Navy; twenty-five Modified Black Swans were launched between 1942 and 1945, including two for the Royal Indian Navy; several other ships were cancelled.