What do you call the Emperor's sons or daughters during the time of the Roman Empire?

Question

I'm referring to some sort of a title (e.g. prince, princess, etc.)

Answer 1

Roman emperors were not hereditary: the title did not automatically pass from father to son, so there were no princesses or princes.

The Roman Senate chose the emperor.

No titles were used, other than the given name (Flavius, Petronicus, Marcus, Lucas, etc.)

Answer 2

I don't think there was any particular title for the children of the emperor. More like the son of (whichever emperor), or Daughter of (whichever emperor). It was when they did get 'in' the actual position of power that the men for example were called imperator.

If you really want to get all complicated, there were ways in which showing respect or showing that a particular woman had a noble heritage through the names.
Cicero is said to have written a letter to a woman called Claudia (Note, that the au in Cicero's, Claudia would have been pronounced as 'aw' Clawdia.) This infliction of the dipthong as 'aw' was meant to be more respectful, and aware of the power she would have had.
It was quite the opposite if Claudia was pronounced with the dipthong becoming 'ow' so Clowdia. It was a 'simplified' form of the name, if you will.

(Hope what I've said makes sense and yes it was slightly off topic, sorry...could resist the addition.)

Answer 3

They were normally just addressed by their name or at times addressed by their name followed by son or daughter of and the Emperor's name.