One of Robertson's main hobbies was flying and, among other aircraft, he owned several de Havilland Tiger Moths, a Messerschmitt Bf 108, and a genuine World War II - era Mk.IX Supermarine Spitfire MK923. His first plane ride was in a Lockheed Model 9 Orion. As a 13-year-old he would clean hangars for airplane rides. He met Paul Mantz, Art Scholl, and Charles Lindbergh while flying at local California airports. His piloting skills helped him get the part as the squadron leader in the British war film 633 Squadron. He entered balloon races, including one in 1964 from the mainland to Catalina Island that ended with him being rescued from the Pacific Ocean.
In 1969, during the civil war conflict in Nigeria, Robertson helped organize an effort to fly food and medical supplies into the area. He also organized flights of supplies to the ravaged country of Ethiopia when it experienced famine in 1978. Within the EAA, he founded the Cliff Robertson Work Experience in 1993, which offers youths the chance to work for flight and ground school instruction.
Robertson was flying a private Beechcraft Baron over New York City on the morning of September 11, 2001. He was directly above the World Trade Center climbing through 7,500 feet when the first Boeing 767 struck. He was instructed by air traffic control to land immediately at the nearest airport after a nationwide order to ground all civilian and commercial aircraft following the attacks.