Unfortunately, none of the Roses donated by the two Pontiffs are currently preserved in the Basilica. It is a possibility that was lost with the Napoleonic invasion of the Papal States, which occurred in 1797.
Starting in the 13th century, the Pontiffs gave the Golden Rose as an expression of gratitude, welcome and hospitality. Furthermore, as a form of gratitude and recognition, it was donated by the Popes over the following centuries to important sovereigns or queens.
The first queen to receive one was Isabella of Castile, in 1493, granted by Pope Innocent VIII. She later received a rose from Mary Stuart of Scotland, at the behest of Pius IV, in 1555.
These were women especially committed to the defense and values of the Catholic Church. However, these roses were also given to certain cities that had fought in defense of the faith.