The Wikipedia article about Faraday cages has this anecdote:
A Faraday cage was used in 2013 by the Vatican to shield the Sistine Chapel from electronic eavesdropping during the secret papal conclave to elect the next pope.
Source: "Papal Election: Vatican Installs Anti-leak Security Devices at the Sistine Chapel". International Business Times. 2013-03-10.
My question is, what would this accomplish? I can see two motivators: they either don't want what they discuss to become public, or they don't want people to have any inclination as to what the decision is leaning towards before it is made.
If it's the first motivator, a Faraday cage won't help. Hardware could be recording and transmit when the cage is removed or be retrieved at a later date. If it's the second motivator, it's probably a better question for the Catholic stackexchange, but I do not know of any reason why this would really matter (are people making huge bets on the outcome? If so, why does the church care?).
Is there some other reason for the use of a Faraday cage I haven't thought of?