Baughman began his career in the 1940s working for his father's company, Thayer Coggin. In the 1950s, he began designing furniture for the company, which eventually led to a fruitful collaboration that lasted over 50 years.
Baughman's designs were characterized by simplicity and elegance, as well as comfort and functionality. He was known for using innovative materials, such as stainless steel and glass, in his designs.
Over the course of his career, Baughman received numerous awards for his work, including the American Institute of Interior Designers' Industrial Design Award of Merit and the American Society of Interior Designers' Award of Merit. Today, his creations are considered collector's items by many design collectors.