Cohen's engineering career began in 1952, when she worked as a junior engineer at North American Aviation. After graduation from USC Viterbi School of Engineering in 1957, she went on to work at Space Technology Laboratories. Space Technology Laboratories eventually became TRW (acquired by Northrop Grumman in 2002). She stayed with the company until her retirement in 1990. Her engineering work included work on the guidance computer for the Minuteman missile and the Abort-Guidance System (AGS) in the Apollo Lunar Module. The AGS played an important role in the safe return of Apollo 13 after an oxygen tank explosion left the Service Module crippled and forced the astronauts to use the Lunar Module as a "lifeboat." Supplies of electrical power and water on the LM were limited and the Primary Guidance and Navigation System used too much water for cooling. As a result, after a major LM descent engine burn two hours past its closest approach to the Moon to shorten the trip home, the AGS was used for most of the return, including two mid-course corrections.  According to her son Neil, "My mother usually considered her work on the Apollo program to be the highlight of her career. When disaster struck the Apollo 13 mission, it was the Abort-Guidance System that brought the astronauts home safely. Judy was there when the Apollo 13 astronauts paid a 'thank you' to the TRW facility in Redondo Beach."

 

In 1990, after retiring from practice as an engineer, she began a publishing company called Cascade Pass with her third husband, David Katz. They published two series of books:

 

The "You Can be a Woman… " series was created to encourage very young girls to pursue careers in science and engineering. The "Green" series focuses on promoting positive environmental practices, aimed at young children. Cascade Pass has sold more than 100,000 of their children's books in these two series.

 

Cascade Pass also published a book called The Women of Apollo (written by Robyn Friend, Cohen's daughter-in-law), which features short biographies of four women who helped put the first man on the moon, Cohen among them.