IPA: /pɒnˈtɪfɪkli/
KK: /pɑnˈtɪfɪkli/
In a manner that is authoritative or dogmatic, often in a way that suggests one is speaking with the authority of a religious leader.
The professor spoke pontifically, as if his opinions were the only valid ones.
Pontifically → It is formed from "pontifex" (from Latin, meaning high priest) and the suffix "-ally" (meaning in a manner). The word "pontifically" refers to something done in the manner of a high priest or with the authority of a pontiff.
Think of a high priest ('pontifex') performing duties in a specific way ('-ally') — that's how you remember that 'pontifically' means in the manner of a high priest.