In 1936, Shusei Nishida and Sueo Oe of Japan tied for second in the pole vault. They were offered a sudden-death jump-off for the silver medal, but the two declined.
For recordkeeping purposes, Oe allowed Nishida to take the silver, as he had cleared the tied height in fewer attempts. Once the two returned to Japan, however, they hired a jeweler to cut the medals in half and fuse them back together.
Half silver, half bronze.
They're now known as the Medals of Friendship. Nishida's medal, shown below, now sits in Waseda University in Tokyo.