In 2001, he received a Technical Achievement Academy Award for “the Fan Descender for accurately and safely arresting the descent of stunt persons in high freefalls”. In 2002, he received the BAFTA Michael Balcon Award.
Armstrong is the brother of Andy Armstrong and husband of stuntwoman Wendy Leech, who is the daughter of fellow James Bond stunt performer George Leech. He met her while filming Superman II (she doubled for Margot Kidder) and they have four children between them. Armstrong has two children from his first marriage, and Leech has a daughter from her first marriage. They have one daughter together.