Last month was the 500th anniversary of the bestowal of the title Defender of the Faith on King Henry VIII by Pope Leo X on October 11th 1521. This was in gratitude for the King’s riposte to Luther the Assertio Septem Sacramentorum - The Defence of the seven Sacraments - which Henry had begin in 1519. There is an article about it at Defence of the Seven Sacraments
Wikipedia has a useful history of the title and its use at Defender of the Faith
Here in Oxford the Ashmolean Museum has what is believed to be the sword sent to the King on this occasion.
The Ashmolean website rather implies it may be English rather than continental in origin, and perhaps that it is a sword of state from the period rather than the Papal gift.
The use of crystal on the hilt is reminiscent of the Crystal Mace at Norwich which was made for the City after its predecessor was lost during Ket’s Rebellion in 1549.
A crystal globe does, of course, feature as the top of the Papally presented Scottish sceptre of 1494, but that may be a feature associated with sceptres, such as the much older Hungarian one.
Unlike the sword the Cap of Maintenance is not known to have survived. The history of this type of insignia, its design and use is outlined in a Wikipedia article at Cap of maintenance
The various pictures of the sword in the Ashmolean appear unwilling in most cases to download. Here however are some details of the crystal hilt from Pinterest: