Nadia and the Mysterious Sea also known as The Secret of Blue Water is an excellent action-adventure story spanning 39 episodes. The series is very Miyazaki-esqe: it centers around Nadia, an orphan circus performer who wears a strange pendant called Blue Water. She is befriended by Jean, a young inventor and coincidentally also an orphan. Blue Water involves them both in a series of adventures connected with the mysterious Captain Nemo and the submarine The Nautilus.
The story is (very loosely) based on Jules Verne's classic novel 20,000 Leagues Under the Sea, and, I would suggest owes some small acknowledgement to another classic: Castle in the Sky, Laputa.