A navis lapidaria at K?z?lburun, TurkeyThe Roman emperor Augustus claimed to have found Rome a city of brick and left it a city of marble (Suet. Aug. 28). Indeed, the remains of more than a dozen stone cargoes in the shallow waters off Italy, France, and Spain attest to the Roman appetite for specialty stones – white marble from Greece and Asia Minor; yellow marble from Numidia; red and gray granite from Egypt. The vast majority of these cargoes, however, have not been treated as coherent archaeological sites; instead they are only superficially explored, their stones partly or wholly salvaged.
As a result, archaeologists know regrettably little about the construction and lading of ancient stone carriers, which must represent some of the most sophisticated technological achievements of the ancient world. It was precisely such ships that brought 16 enormous monolithic granite columns, each nearly 40 feet tall, from Alexandria to Rome for the façade of Hadrian's Pantheon. A century earlier, the emperor Caligula arranged for the transport to Rome of a massive 320-ton obelisk . The historian Pliny, upon viewing the ship that delivered the obelisk, described it as "the most amazing vessel that had ever been seen on the sea (NH 36.70)."
A 320-ton obelisk would require a ship of at least 400 tons displacement or 363 cubic meters displaced water. If you figure the ship was 60 meters long and drew 1.5 meters of depth you get a beam of 4 meters, so these rough dimensions aren't too bad. But I'm probably off a fair bit in only assigning the ship an empty weight of 80 tons, could be double or triple that because of balast, freeboard, decking, lead plate, etc.
Nevertheless, A Nemi ship would have been in that size range, so they were well capable of atlantic crossing.