Four hundred years after Michelangelo Merisi, the painter known as Caravaggio, died in this coastal Tuscan town — wretched, feverish and on the run from numerous enemies — what are said to be his remains received a hero’s welcome on Saturday.

Laid on a red velvet cushion inside a transparent case, the bones — fragments of the cranium, an incomplete femur, and part of a bone from the base of the spine — reached the port on a striking tall ship, greeted by a small crowd clapping and cheering.

“When we first began, people thought we were mad,” Silvano Vinceti, the president of the group that sought to identify the bones of the 17th-century painter, told the dignitaries and townsfolk gathered at the pier. “But this kind of madness is the very salt that now allows Italians to offer the world something exalting from a scientific point of view,” he said to more cheers....