ZURICH—The Slovenian government has turned Brdo Castle into a prominent stage for international diplomacy, including a storied meeting between Presidents George W. Bush and Vladimir Putin. Now members of Yugoslavia’s deposed royal family want the publicly owned castle back—or at least compensation for what they see as a decades-old theft of their property.

“Everyone goes there,” 80-year-old Princess Elizabeth of Yugoslavia said during a recent interview. “Nobody knows the truth behind it.”

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