Cospi’s father died in Bologna in 1624, and he inherited the family property and position.
 He became the representative of the Grand Duke Ferdinando II in Bologna.
This involved formal diplomatic services and attendance at functions and ceremonies.
 He mediated between the Bolognese and Tuscan authorities, and promoted trade and the interests of Florence in Bologna.
He also helped the Medicis to obtain the services of Bolognese artists.

In 1637 Cospi married Smeralda di Annibale Banzi.

They had just one daughter, Dorotea, 
although Cospi was said to have had a child in Florence whom the Granduchess Vittoria della Rovere accepted as one of her court ladies.

As the value of his services increased, the Grand Duke increased Cospi’s salary and in 1641 made him bailiff of Arezzo within the Order of St. Stephen.
In 1643 Cospi escorted the new Cardinal Giancarlo de' Medici to Rome to receive his cap.
In 1646 he undertook a mission to Milan to pay respects on behalf of the Grand Duke to the new governor, Bernardino Fernández de Velasco, 6th Duke of Frías.
Two years later he was given the hereditary title of Marquis of Petriolo.
On 9 May 1650 he became a senator of Bologna.
 The next year he made another trip for the Cardinal Giancarlo de' Medici to pay his respects to Mariana of Austria, the new Queen of Spain.
 In 1664, 1665 and 1672 he was Gonfaloniere of Bologna.

In 1673 Cospi  resigned from the office of senator, but continued to take part in public life.
 
He died in Bologna on 19 January 1686 and was buried in San Petronio in the family chapel.
Cospi’s father died in Bologna in 1624, and he inherited the family property and position.  He became the representative of the Grand Duke Ferdinando II in Bologna. This involved formal diplomatic services and attendance at functions and ceremonies.  He mediated between the Bolognese and Tuscan authorities, and promoted trade and the interests of Florence in Bologna. He also helped the Medicis to obtain the services of Bolognese artists.
In 1637 Cospi married Smeralda di Annibale Banzi.
They had just one daughter, Dorotea, 
although Cospi was said to have had a child in Florence whom the Granduchess Vittoria della Rovere accepted as one of her court ladies.
As the value of his services increased, the Grand Duke increased Cospi’s salary and in 1641 made him bailiff of Arezzo within the Order of St. Stephen. In 1643 Cospi escorted the new Cardinal Giancarlo de' Medici to Rome to receive his cap. In 1646 he undertook a mission to Milan to pay respects on behalf of the Grand Duke to the new governor, Bernardino Fernández de Velasco, 6th Duke of Frías. Two years later he was given the hereditary title of Marquis of Petriolo. On 9 May 1650 he became a senator of Bologna.  The next year he made another trip for the Cardinal Giancarlo de' Medici to pay his respects to Mariana of Austria, the new Queen of Spain.  In 1664, 1665 and 1672 he was Gonfaloniere of Bologna.
In 1673 Cospi  resigned from the office of senator, but continued to take part in public life.  
He died in Bologna on 19 January 1686 and was buried in San Petronio in the family chapel.
Ferdinando Cospi