I should know better than to get into this at all... but... one of the great things about these restaurants on the Millennium Class ships is their remarkable wine lists. I'm not sure you'd want to bring your own bottle into that elegant venue. If you have a particularly good favorite wine, I suppose I'd bring it down to them early in the day and pay the corkage fee. I wouldn't feel comfortable carrying it down with me. Check out their wine list. It is quite good and fairly priced.
We had a bottle of champagne that we asked about having served to us in the S.S. United States Restaurant. The answer was a very polite no. You can do that in the Trellis, but not S.S. United States.
Reservations? YES! Make them as soon as you board and expect to wait quite a while to make them. Dress-up? YES!
I recommend reserving for an at-sea day so you don't have to rush back from a port call before this special evening. When we were on Millie, we had the opportunity to spend an hour or so in the morning in the Olympic Restaurant, talking with staff and watching the prep for the evening. The Maitre d', Roberto, gave us specific instructions on how to eat lightly for the rest of the day. "Just fruit and a roll for lunch, Madame. You do not want to spoil your appetite."
The food is top-notch, the wines divine, and the service equal to any fine restaurant anywhere. Don't miss the goat cheese souffle.
pamda -- CM First-Time Cruisers Editor and Serious Foodie