If you’re going to strut como La Jefa, then you’re going to need a backing track.

The new limited series Griselda stars Sofía Vergara as devoted mother and savvy and ambitious businesswoman Griselda Blanco. Inspired by the real-life “Godmother,” the story follows her rise through the Miami crime world to create one of the most profitable cartels in history. And that smoky setting needed music to match the allure of ’70s and ’80s Miami. “There’s such a wealth of great music from this period, and to be period accurate in this case was pretty easy because a lot of these songs are incredibly well known,” said creator and executive producer Eric Newman.

From David Bowie’s “Let’s Dance” to Donna Summer’s “Hot Stuff,” the music in Griselda is meant to feel very much of a recognizable time and place. In addition to Latin and Caribbean music,...