I was on the Dec 18-26 sailing of Celebrity Solstice, and not only was there a separate vegan menu, but found the crew well informed about vegan dietary requirements, and eager to keep me well fed
At the time of my booking, I had my travel agent inform Celebrity that I was a vegan (you can do this on your own if not using a travel agent), and on the day of embarkation, I introduced myself to the maitre d'. He smiled, took out a vegetarian menu, and went over it with me, discussing which dishes I could eat as is, and which the chef could modify for me (and how he would do so). The dishes I chose would be my dinner that night, and he told me that each evening I would be shown the vegetarian menu for the next night, and place my order in advance. (Note: I don't eat sweets, so asked to be served melon and berries each night for dessert, however I was told that desserts would be prepared without honey.)
I switched tables, but it wasn't an issue, because the vegetarian menu was linked to my room number, not my seating assignment (during the cruise I met someone who was on a low sodium diet, and who had open seating, and he also had no issues).
To my surprise, on the third night, the fancy vegetarian menu was replaced with a printed sheet that was headed 'vegan menu'. It was actually more a vegetarian menu, but when I pointed that out to the maitre d', he told me that the chef would prepare any dish on it to match vegan requirements.
There were always 2 or 3 choices for each course, and all were delicious (except for one night, when the dish I chose was so spicy (and I love spicy foods) that it burned my lips at the first bite, and I gave up after a few more bites! )
The lunch buffet also was a delight- the first day, I was spotted looking around with an empty plate, and was approached by a maitre d'. When I told him I was a vegan, he asked what type of food interested me, and I pointed out that the Indian section looked inviting (there was an 'Indian curry' station each day, with several selections). He placed a call to the chef in charge of that station, who happily pointed out the dishes that were prepared vegan (they were delicious!).
The next day at the buffet (and each day following), a maitre d' found me,
and patiently and pleasantly made sure I found plenty to eat. What a delight!
BTW- in addition to the hot foods, each day at the buffet there were both a salad station which contained a rotating selection of about 20 different cut vegetables, beans, and grains, and also a fruit station with a selection of cut melon as well as a huge bowl of fresh fruit salad, and also several whole fruits. There was also another area with dried fruit and nuts.
It was so nice to not only have no issue with food, but to have such delicious meals that I'm planning (and looking forward to) cruising Celebrity again and again.