A similar sense of timelessness also permeates the garden, which includes a grove of orange and lemon trees, as well as a long colonnade leading to a terrace overlooking the sea. “The garden had been abandoned, but it was still among the most beautiful I’d ever seen,” says garden designer Antonella Sartogo, who was charged with revitalizing it. “The owner gave me free hand,” she says, “so long as I read Flora Privata di Capri by Edwin Cerio”—an engineer and naturalist born on the island in…