Willoughby taught for many years at Oberlin College, where he was the first Robert Wheeler Professor of Performance.

He taught for ten years at the Peabody Institute,[2] and later at the Longy School of Music of Bard College.

He received the Alumni Achievement Award from Eastman School of Music[3] and in 1996 he received a Lifetime Achievement Award from the National Flute Association.

[4] Among his many students is the jazz flute player Paul Horn.

[5] Robert Willoughby, flute James Caldwell, oboe Lawrence McDonald, clarinet Robert Fries, French horn Kenneth Moore, bassoon Saturday, January 14, 1984, 8:00 p.m. in Hamman Hall, Rice University Digital Scholarship Archive http://scholarship.rice.edu/handle/1911/76867 He married author Elaine Macmann Willoughby in 1957.