The Congressional Gold Medal, along with the Presidential Medal of Freedom, is the highest civilian award in the United States. Initially, recipients of the medal were all military figures honored for their service in the Revolutionary War, War of 1812, and the Mexican-American War, but the scope of the medal has since been broadened to honor achievements by explorers, musicians, athletes, activists, scientists, and more. Each medal is designed by the U.S. Mint to commemorate the specific person and achievement for which the medal is awarded.
The U.S. Mint also sometimes produces bronze replicas of the gold medals, but we can't say for sure if these particular copies were made in 1814, or were made in 1914 to commemorate the centennial.
Obverse of Macdonough's medal: THO. MACDONOUGH. STAGNO CHAMPLAIN CLAS. REG. BRIT. SUPERAVIT. (Thomas Macdonough Stagno Champlain classim Regis Britannia superavit: Thomas Macdonough defeated the Royal British fleet on Lake Champlain.)
Reverse: UNO LATERE PERCUSSO. ALTERUM IMPAVIDE VERTIT. (Beaten on one side, he fearlessly turns the other.) Naval action on Lake Champlain, between the United States fleet, carrying eighty-six guns, under Captain Macdonough, and the British fleet, with ninety-five guns, commanded by Commodore Downie. To the right, the city of Plattsburgh in flames. Exergue: INTER CLASS. AMERI. ET BRIT. DIE XI SEPT. MDCCCXIIII. (Inter classim Americanam et Britannicam, die 11 Septembris, 1814: Between the American and British fleets, September 11, 1814.)
Captain Robert Henley of the Eagle and Lieutenant Stephen Cassin of the Ticonderoga also received gold medals in October 1814 for their role in the "decisive and splendid victory gained on Lake Champlain." Congress also requested that the President "present a silver medal, with suitable emblems and devices, to each of the commissioned officers of the navy and army serving on board, and a sword to each of the midshipmen and sailing-masters, who so nobly distinguished themselves in that memorable conflict."
Obverse of Macomb's medal: MAJOR GENERAL ALEXANDER MACOMB. Bust of General Macomb, in uniform, facing the right.
Reverse: RESOLUTION OF CONGRESS NOVEMBER 3. 1814. The American army repulsing the British troops, who are striving to cross the Saranac river. To the left, Plattsburgh in flames; to the right, naval battle on Lake Champlain; in the distance, Cumberland Head. Exergue: BATTLE OF PLATTSBURGH SEPT. (September) 11. 1814.
The third medal in our display is one that was produced for the Centennial Celebration of the Battle of Plattsburgh in 1914, and honors both Macdonough and Macomb. Their portraits seem to be modeled upon those used for the Congressional Medals; the reverse shows a naval scene and a version of the New York State seal.
Thanks to the Press-Republican for providing the name of the manufacturer and helping to solve part of this mystery! Information about Whitehead & Hoag was found at tedhake.com and oldnewark.com.
Information about the Congressional Medals was taken from The Medallic History of the United States of America, 1776-1876, by J. F. Loubat. You can read it online via Project Gutenberg.