Ovid was a special case, and it wasn't that he was banished from the Empire, but rather he was banished to Tomi, which, while a border town, was in fact included in the empire. Brill's New Pauly mentions it came under Roman control in 70 BCE. I can't find any information about a formal judgment against Ovid; as far as I know we just have the "carmen et error" line for understanding his exile. I'm willing to bet that like so much else Augustus did this exile was what would seem to us to be an informal arrangement. Ovid specifically says there wasn't official action taken. From Tristia 2 (somewhere around the 100 line mark)

You didn’t condemn my action by Senate decree, nor was my banishment ordered by special court. With stern invective – worthy of a prince – you yourself, as is right, avenged the offence.

It looks like he got a stern talking-to and knew what was good for him (i.e. not living in Rome).

Traditionally, until 70 BCE, banishment meant banishment from the city of Rome defined as the area included in the pomerium, the sacred line that defined the city limits, and was a voluntary act. Exiles could park themselves in the outskirts past this line; only sometime after the Social War (91-89 BCE - in my opinion 70 seems like a good option) were exiles driven out of Italy entirely, and then they were free to wander wherever. So you will find people like Milo hanging out and enjoying the oysters of Marseille.

If I'm reading Kelly, A History of Exile in the Roman Republic correctly, the last known exile to stay in Italy was Q. Fabius Maximus Eburnus (exiled ca. 104 BCE).

The traditional mechanism for enforcement was "aquae et ignis interdictio;" no one is allowed to supply the exile water or shelter inside Rome, and then Italy after, as I suggest, 70 BCE. And that's it. There's no formal police force keeping exiles away. It's really a matter of being excluded from the political community, which is why Ovid is a strange case.