Criticism of the emperors were always written after the death of the emperor, so historians certainly feared the emperors wrath. An example of censorship is the exile of Ovid, although it is uncertain why he was exiled, it is assumed that it was due to his raunchy poems that went against the traditional roman ideals Augustus was trying to re introduce to Roman Society.

The emperor Caracalla, after his ascension to the position, removed all mention of his hated brother Getta from monuments in Rome, famously the Severian arch, were Getta's name has been scraped off.

Obviously these were not very succesful, as we still know who Getta is, and still have copies of Ovid's poems. Censorship was certainly common in Rome, but it was not often carried out across emperors reigns.