The Romans never contemplated crossing the Atlantic. They were, however, quite interested in exploring its more accessible corners, particularly after the conquest of Britain. Plutarch mentions that one of his friends - the scholar Demetrius of Tarsus - was commissioned by the emperor to explore some remote islands off the British coast (probably the Isles of Scilly):

"Demetrius said that among the islands lying near Britain were many isolated, having few or no inhabitants, some of which bore the names of divinities or heroes. He himself, by the emperor's order, had made a voyage for inquiry and observation to the nearest of these islands which had only a few inhabitants, holy men who were all held inviolate by the Britons." (On the Failure of the Oracles 18)

Around the same time (the late first century CE), the Romans sent a naval expedition to circumnavigate Britain (replicating the voyage of Pytheas four hundred years earlier):

"Round these coasts of remotest ocean the Roman fleet then for the first time sailed, ascertained that Britain is an island, and simultaneously discovered and conquered what are called the Orcades [Orkney Islands], islands hitherto unknown. Thule too was descried in the distance, which as yet had been hidden by the snows of winter." (Tactius, Agricola 10)

Centuries earlier, the historian Polybius, sailing under the auspices of his patron Scipio, had ventured down the west coast of Africa. Unfortunately, we know nothing about the particulars - and in any case, Polybius' aim was to learn more about Africa, not the Atlantic.

There seem to have been occasional voyages in the Roman era to the "Fortunate Islands" (the Canaries). Yet to judge from the description Pliny the Elder gives of them (in which both their size and their distance from Spain are vastly exaggerated), they were known mostly from hearsay. The Republican general Sertorius supposedly considered fleeing to the islands and settling there; but we never hear of any officially-sponsored expedition or colonization effort.

So why didn't the Romans try to explore further? First, there were the real hazards of ancient sailing, which led most captains to stay within sight of shore whenever they could. Second, there were the imagined dangers of unknown seas. Hearsay placed great mats of ship-snaring seaweed and strange sluggish currents in the western seas; and the Romans had no charts or reliable reports to set against such rumors. Finally and most importantly, neither the Roman government nor Roman merchants had any incentive to strike off into the unknown. Even if they believed Eratosthenes, and thought that it was theoretically possible to sail from Spain to India, they had no evidence that anything lay beyond the outer sea.