I've been trying to track down the Quintus Servilius Pudens (or 'Mr. Modest') mentioned in the article below. As he is said to have been a friend of Hadrian, the following is the individual closest to the necessary dates I've been able to find. The only year mentioned in the entry is 111, still during the reign of Trajan, so if this is our Servilius, he must have lived on into the reign of Hadrian. Is this he?
The entry is from Paulys Realencylopädie Supplement IX, entry 77a.
Q. Servilius Pudens, ein Legat, der mit Plinius im Dez. 111 in Nicomedia zusammentraf (Plin. epist. X 25), vielleicht Vater des cos. 166 (s.u. 77b). Er wird auf den Ziegeln CIL XV 346. 349-50. 1429-41 erwähnt.
The (possible) son mentioned was also named Q. Servilius Pudens, consul ordinarius in 166 with L. Fufidius Pollio and proconsul of Africa around 180 or shortly thereafter.