Answer : nos despedimos
Entire sentence : Nosotros nos despedimos en el aeropuerto.
Explanation : The subject of this sentence is "Nosotros", first plural person, so the verb must be conjugated in first plural person too. As it is a reflexive verb the corresponding indirect object pronoun is "nos" which means "a nosotros".
Hope this helps!
[tex]\textit{\textbf{Spymore}}[/tex]