Ceremoniously means “in a ceremonious way”: you do something with formal, serious manners, as if the moment were a small ceremony. Someone may ceremoniously open a gift, or ceremoniously hand over a key. It is not a playground word; you meet it in stories and in slightly fancy writing. Though actually, writers often use it with a twinkle. The person is making a show of the act — a little too grand for the room. The meaning is the same idea as ceremonious; this form just tells you how the action is done.