Having perhaps had a little fun with some of the less plausible evidence of contact between the Americas and the world of Antiquity, it should be noted that there are a few enigmatic clues that suggest that just maybe a few Romans made it to these distant shores.
The most plausible scenario would be storm tossed mariners remarkably surviving an ocean crossing in ships designed to rarely leave sight of land. It exceeds credulity to imagine any of them being brave enough to try a reverse journey to tell of their experience.
But perhaps they might bring a few things with them, exotic artifacts to the indigenous peoples. The Round Rock Mound coin could be such an item. As could this:
Dating techniques are not specific enough to help much, but stylistically this indeed appears to be of Roman origin. The beard alone makes a Meso American manufacture seem implausible.
Calixtlahuaca's head has generated a bit of controversy. A fair summary of same can be found Here
As to its site of manufacture there seems little doubt; scoffers point to the possibility of an archeological prank gone awry, or to chaotic artifact storage allowing for a mix up. Probably there will be no satisfactory resolution to this debate.
If this was a Roman artifact somehow making it halfway around the world, where would it have arrived? Although there are a few who suggest trans Pacific contact, the likely route would have been trans Atlantic. And just maybe a potential land fall was at Guranbara Bay, near Rio de Janeiro. Supposedly in the 1970s fishermen kept snagging their nets on an underwater wreck. They eventually hauled up some heavy earthenware jars that they broke up, feeling they might be "macumba jars" used in voodoo ceremonies. Later scuba divers recovered a few more jars and sold several to tourists. The Brazilian police intervened, and confiscated two jars which are said to be of Roman origin. See this somewhat rambling discussion for more details Romans do Rio.
Interestingly when researching possible points of origin for a wrecked Roman trading ship I looked at the suggested Cape Verde islands off the coast of Africa and found zero evidence of Roman contact. The closest confirmed jumping off point would have been the Canary islands where there was at least a modest degree of Roman presence/trading. One red flag popped up right away when reading about Roman pottery in the Canaries
"In 1964 a Roman amphora was discovered in waters off Lanzarote, and since then a number of others have been found underwater. All, however, lacked proper context and could not be dated precisely; that they were truly Roman was also questioned because many were similar to amphorae used by the Spanish in the sixteenth century for trade with the Americas. The finds from El Bebedero show that Romans did trade with the Canaries, though there is no evidence of their ever settling there. "
So....it sounds as if there were still some amphora like vessels being used in the early days of Spanish trade with the Americas. And since the Guranbara wreck has mysteriously been declared off limits for unknown reasons we are left with a few pottery shards and little more.
So with current archeological information we can at best entertain the notion of a few hungry and bedraggled Roman mariners washing up on the shores of a New World. But they obviously did not spark a Renaissance that opened the riches of the West through a mythical Province of Occidentia.
No, the poor fellows found themselves permanently marooned in a land where the grape was unknown, and where syphillis existed in a virulent form that would wreak havoc in Europe when contact was eventually made by Columbus.
Denied the pleasures of both Bacchus and Venus their lives would have been Hobbesian indeed..."solitary, poore, nasty, brutish and short".