Congressional Tribute to Constance Baker Motley Act of 2013 - Authorizes the President Pro Tempore of the Senate and the Speaker of the House of Representatives to make appropriate arrangements for the posthumous presentation, on behalf of Congress, of a gold medal in commemoration of Constance Baker Motley (civil rights attorney at the National Association for the Advancement of Colored People Legal Defense and Educational Fund, Inc., first African-American woman elected to the New York State Senate, and Chief Judge on the U.S. District Court for the Southern District of New York), in recognition of her enduring contributions and service to the United States.