Adm. Petersen was awarded the Navy Cross, the service's highest Navy decoration for valor after the Medal of Honor, for his role during World War II in defending the aircraft carrier Hornet against enemy air attack and subsequently in rescuing survivors, after a decision had been made to abandon the ship, during the Battle of Santa Cruz Islands in October 1942.
Serving as commanding officer of the destroyer Mustin, he brought his ship alongside the disabled and listing carrier while under heavy Japanese attack to help in fighting fires and assist in damage control, according to the citation accompanying the Navy Cross. He rescued 337 survivors from the Hornet, then fired the torpedoes that scuttled the ship.