The Sweating Cenotaph at the Archbasilica San Giovanni in Laterano

This former papal palace houses an unusual monument- Pope Sylvester II's cenotaph (a funeral moment for a person whose remains are entombed elsewhere) that's said to sweat profusely when the death of a pope is near. If it's clammy or damp, the death of a cardinal or bishop is immanent. 

Interestingly, Pope Sylvester II has long been associated with the supernatural. His contemporaries (likely amazed by and maybe jealous of his intellect) said he was a sorcerer who built an automaton which acted like an oracle. The automaton told him that if he ever went to Jerusalem he would be taken by the devil. Taking the warning literally, he avoided the Holy Land but was struck dead when he said mass at Santa Croce in Gerusalemme, a basilica just down the street from San Giovanni in Laterano. His remains are still there and an alternate version of the legend says his bones rattle when a pope is about to die.

San Giovanni in Laterano was also the site of the Cadaver Synod in 897 when the rotting corpse of Pope Formosus was dug up and put on trial by Pope Stephen VI. Records show that an earthquake damaged the church during the trial and shortly after it concluded a fire nearly destroyed it completely. These events are usually viewed within the church as a sign of God's displeasure with the macabre spectacle.