Answer: Yes, we have the answer!! From Vatican Notes (Volume VIII Issue 6 (May-June 1959) Page 5) we learn that St. Charles Borromeo was a favorite saint of Pope John XXIII. It was on St. Borromeo's feast day (November 4th, 1958) Pope John XXIII's coronation took place. St. Charles Borromeo was the Archbishop of Milan from 1564 to 1584 and a leading figure of the Counter-Reformation combat against the Protestant Reformation. He was responsible for significant reforms in the Catholic Church.

      
Pope John XXIII Coronation Issue, Scott # 250-253 (1959)

See: Commemorative Issue For The Coronation of Pope John XXIII Vatican Notes Volume 07, Issue 6 (May June 1959) Pages 5-8