Miglietta would recount that on the day he was to be appointed Archbishop of Conza-Sant'Angelo dei Lombardi-Bisaccia, Pope Paul VI died. Therefore, his appointment had to be postponed until the election of Pope John Paul I, who was then unable to sign the appointment due to his sudden death. Finally, on 18 November 1978, Pope John Paul II appointed him to the archbishopric. Shortly after being made archbishop, Miglietta suffered a heart attack, which was followed by the devastating Irpinia earthquake of 1980. His time as archbishop involved ministering to the victims of the earthquake.