1. To issue an authoritative pronouncement or declaration about something. The boss always pronounces on whatever is happening in the news like he's some kind of authority on current events. We waited with bated breath for the judge to pronounce on the case.

2. To deliver a particular authoritative opinion or judgment about something. In this usage, a noun or pronoun is used between "pronounce" and "on." You don't need to pronounce your opinion on every little thing the kids do, Tom—give them a bit of room to navigate these things on their own. We sighed with relief when she pronounced her verdict on the case.