I just googled "dinner with the captain"
The cruise companies seem to sell the idea as a "great maritime tradition" -they don't mention the great maritime tradition of the captain going down with the ship of course. Specially invited guests thrill to the thought of being invited to the captain's table .Some cruise lines have a lottery for who gets a seat .Kendall wrote that the captain is always responsible when the ship is at sea , but I wonder whether a captain's duty as a mariner and his role as the manager of a floating pleasure palace don't sometimes clash .

This is the sort of stuff you get :
"Our captain always enjoyed a cocktail or two before dinner. When he was fairly well fortified, he would appear at the table about 20 minutes after the rest had entered."
"The evening begins with cocktails, either in a reserved area of a public lounge or the Captain's quarters, where the Social Hostess greets you and makes introductions to the Captain and other high-ranking officers. After getting acquainted, you are escorted to the Captain's table and take your place according to pre-arranged seating."
"Then sit back and enjoy a sumptuous dinner with exquisite service and fine wines. A photographer will appear to preserve the memories and the picture will be delivered to you the next day, perhaps with a copy of the menu or a note of thanks."