If you ever listen to talk radio you'll hear some fairly pontifical talk going on — that is, puffed up, vain, overblown speech from someone convinced he alone is right. What he's doing is pontificating.
Pontifical also has a strictly religious meaning, in the sense of anything related to the Pope since the Pope is also known as the Pontiff, or supreme head of the Roman Catholic church. Because Catholic doctrine regards the Pope as being incapable of being wrong, his pontifical utterances are therefore deemed quite infallible.
