Miles was born in Nice, France, the daughter of Jeanne Miles, an American painter, and Johannes Schiefer, a French painter and art curator. She immigrated to the United States, and was naturalized a citizen, in 1941. She was a graduate of The Putney School, a progressive independent high school in Putney, Vermont in 1958.
Miles won the two Emmy Awards for her portrayal of Laura Wingfield in the 1973 production of Tennessee Williams' The Glass Menagerie: Best Supporting Actress in Drama (for a Special - Program, a One-Time Appearance in a Series - or a Continuing Role) and Supporting Actress of the Year.
She has also played supporting roles in various movies, including The Way We Live Now (1970), Bug (1975), The Ultimate Warrior (1975), The Dark Secret of Harvest Home (1978), Cross Creek (1983), Rosencrantz & Guildenstern are Dead (1990), Above Suspicion (1995) and Judge Dredd (1995). She is known to Star Trek: The Next Generation fans as Perrin, Sarek's wife, from the episodes Sarek and Unification. In 2001, she had a secondary role as the wife of a storekeeper in Tom Selleck's Turner Network Television Western film, Crossfire Trail.
She was also in an episode of The Incredible Hulk entitled “The Quiet Room” and in the episode “Murder on the Flip Side” of the NBC crime drama The Eddie Capra Mysteries.