Since 1979, the Emmy Awards have made space, between the many live-action series it honors, to hand out some recognition to animated programs through its Outstanding Animated Program category. But in the nearly 50-year history of the trophy, a large, increasingly important subset of the medium hasn’t even been eligible to compete: anime.

The rules for the Emmy Awards state that, for a show to be submitted in the Primetime Emmys ceremony, the show needs to be produced at least partially by an American company. As a result, the uniquely Japanese art form — despite its growing popularity in the West — has only been able to compete in the international category for “Best Kids Animation.”

Six series produced in Japan have been nominated in that category since 2012: “Digimon Xros Wars,” “Ronja, the Robber’s Daughter,” “Shimajiro’s Wow!,” “Design Ah!,” “To Your Eternity,” and “Rilakkuma’s Theme Park Adventure”; “Ronja, the Robber’s Daughter...