TALAMONE, Italy — As the Sirena brought its passengers back to port, Paolo Fanciulli paused from spreading his nets and sustainable fishing gospel to point at an empty spot of sea.

“There, below the lighthouse,” said Mr. Fanciulli, clad in his rib-high yellow waders. “The sculptures are there.”

About 25 feet below the rippling surface of this rocky promontory on the southern Tuscan coast, schools of fish visited a museum of four marble blocks, mined from Michelangelo’s preferred quarry and sculpted by acclaimed artists.