Miranda was born to Barry and Lindsay Otto in Brisbane, Australia. Both parents were actors, though Miranda's mother quit acting upon Miranda's birth. When her parents separated in 1973, Miranda lived with her mother but spent weekends and holidays with her father.
In 1990, Miranda graduated from the prestigious National Institute of Dramatic Arts (NIDA). She appeared in several movies in Australia and was nominated five times for an Australian Film Institute Award. In 2003, Miranda was nominated for a Helpmann Award for her role in the stage performance of A Doll's House. In 2005, Miranda received a Logie Award for her role in a television miniseries. In the U.S., Miranda was nominated for an Academy of Science Fiction, Fantasy and Horror Films Award for her role as Eowyn in the Lord of the Ring trilogy.
On January 1, 2003, Miranda married Australian actor, Peter O'Brien, whom she met in 2002 when they both performed in A Doll's House. In 2005, Miranda give birth to their daughter, Darcey. When not working, they reside in Australia.