In Rome there are two special items on restaurant and bar bills that are often confused with a "forced" tip, but which actually have nothing to do with it:
On the one hand, the "coperto", a kind of basic fee of 1-3€ per person, which is charged for place settings, bread etc. in restaurants regardless of your consumption. But coperto does not end up in the waiter's purse.
On the other hand "servicio", a service fee, which is charged in bars and cafes where you also have the possibility to consume your snacks and drinks directly at the bar without service. Servicio is also not handed down to the waiters.
So if you were satisfied with the service and would like to tip, that is welcome (around 10%), but is not expected. Italians themselves tend to tip less in international comparison. It's best to leave your tip on the same tray as the bill and your change after you've received it.