Born and raised in Bologna, Perdisa was the son of Luigi Perdisa, a professor and faculty dean at the University of Bologna, founder of the agricultural publishing house Edagricole, and editor of the agricultural magazine Terra e Vita. Luigi Perdisa was later awarded the Knight of the Order of Merit for Labour in 1976. Cesare's brother Sergio followed their father's path into agricultural publishing, while Cesare pursued motorsport.
Perdisa made his Formula One debut at the 1955 Monaco Grand Prix, driving for Maserati. He finished third in a shared drive alongside Jean Behra, earning a podium on his first championship appearance. He was notably younger than most of the drivers competing at the time, and formed a friendship with similarly youthful Eugenio Castellotti, a bond that would later shape the course of his career.
A second podium came at the 1956 Belgian Grand Prix in another shared drive, this time with Stirling Moss. On lap eleven, Moss lost the right rear wheel of his Maserati and ran back to the pits on foot, taking over Perdisa's car and driving it to the finish. The shared result counted as a podium for both drivers.
Throughout his career, Perdisa was regularly asked to cede his car to more experienced teammates when they encountered mechanical problems — a role that reflected both the team structures of the era and his own accommodating temperament. At the 1957 Argentine Grand Prix, driving a Ferrari Lancia D50, he gave his car first to Wolfgang von Trips and then to Peter Collins in an unsuccessful attempt to prevent Juan Manuel Fangio from winning on his Maserati. The trio finished sixth.
Perdisa had entered the 1957 12 Hours of Sebring but withdrew after learning of the death of Eugenio Castellotti, who had been killed while testing a Ferrari at the Modena Autodrome. Shaken by the loss, Perdisa initially described his decision to withdraw as temporary, but he was unable to return to racing and eventually retired permanently.
In September 1957, Perdisa made brief news when he transported Juan Manuel Fangio and Fangio's partner to a hospital in Bologna after the couple's Lancia Aurelia was involved in a high-speed road accident. Both Fangio and his companion survived with minor injuries.
Following their father's retirement in the mid-1960s, Perdisa and his brother Sergio continued to publish Terra e Vita. The magazine was eventually sold to Calderini Agricole, Italy's largest agricultural company. Perdisa died on 10 May 1998.
Though his Formula One career spanned only eight races, Perdisa's two podium finishes and his association with the early Maserati and Ferrari efforts of the mid-1950s give him a clear place in the history of the sport's formative championship years. His friendship with Castellotti and the manner of his retirement speak to the personal costs that were inseparable from racing in that era.