Irish coats of arms have been granted to presidents John F. Kennedy and Bill Clinton, but the Garter King of Arms in London says they're not worth the vellum they're printed on.
Guy Power, a civil servant with Nasa in California, wrote to the College of Arms in London asking it to reregister a grant of arms made by the Irish chief herald in 1981. Peter Gwynn-Jones, the Garter, replied that this posed a considerable difficulty.
In a letter to Power he said an order made in 1943 by the Irish government “did not include any explicit measure empowering the new chief herald to grant armorial bearings”. He noted that several recent judgments also indicated that powers the Irish state thought it had “have no such origin”. [Link]