Yo-Jin-Bo ~ The Bodyguards

The story focuses on Sayori, a modern-day school girl with an interest in history. She joins her history club in an excavation, and discovers an old Jade pendant buried in the mud and takes it home with her. That night, the pendant comes to life, glowing a weird green and putting Sayori in touch with the ghost of a princess named Hatsuhime, who used to live in the castle that the club was excavating.

[Edited from LadyRhian's review]