The last couple of years notable Science Fiction/Fantasy Films have been nominated in the shorts categories.
Last year it was Death of a Shadow. The previous year there was the very funny Time Freak (Which I am still waiting for at any Marathon.)

Went to see shorts programs again this year.
Not the best film, but a great one joke live action short short starring Martin Freeman, The Voorman Problem was very enjoyable. It deals with the God problem.
Almost all animateds qualify as fantasy. I really enjoyed Mr. Hublot a cute fantasy of a man and his dog in a beautifully depicted steampunk mechanical universe. Also of note was Possessions, an anime ghost story that was visually beautiful.
Personally, I'd pick Hublot for the Oscar. Unfortunately, it won't win over a Disney, Mickey cartoon. Voorman, although cute, will lose to one of two profoundly disturbing films, one depicting a woman fleeing an abuser and another on child soldiers in Africa.
Haven't seen the nominated documentaries as yet. But if you are a lover of film, find some place that is showing any of the Oscar shorts programs. With the hundreds or thousands made each year, the quality is far beyond that of almost all feature length films.