Are there any objects that are still extant that we know (fairly definitively) that a famous person from classical antiquity actually held or touched (not just gazed upon)? Ideally someone very famous (e.g., Augustus, Alexander the Great, Socrates, Cleopatra, et al.), but if that's not likely than maybe some of lesser importance.
Oh, I should mention that I do know of the cup of Phidias found in his workshop at Olympia. While it's not 100% certain that it was his, it does seem likely. It has the possessive form of his name on it (Pheidiou), implying that it was his. While he's no JC, he's still well known.
It may be a bit if a stretch to call it classical antiquity, but it's pretty close. The Iron Crown of Lombardy, though it has been reworked and modified over time, does appear at its base to be the crown with which Charlemagne was crowned in Lombardy. It is older than him, but he's probably the biggest name to have worn it.
There is a papyrus from the court of Cleopatra, where, after the main text written by a scribe, there is appended a single word in another hand: ginesthoi, which translates as something like "Make it so!"
It's been theorized the last word may have been written by Cleopatra herself approving the letter, however obviously it is not possible to know for sure, especially since her actual name doesn't appear
http://archive.archaeology.org/0101/newsbriefs/cleopatra.html