Yes they do. An afternoon party with dancing, cake and champagne if I remember right on our 40th. But be sure to inform Celebrity through your TA that you'll be celebrating yours while aboard. That way you'll have an invitation waiting for you. We will be celebrating our 44th on the Summit this year. Have fun!!
We have celebrated many anniversaries on board a Celebrity cruise. Hubby would usually arrange for a cake. On one cruise, he went all out. At dinner that night, he had arranged for my gift and cards to be delivered with desert - my gift (a beautiful opal and tanzanite ring) was on a covered plate. Somehow without my realizing it, he managed to get our camera to the asst. waiter for pictures as the waiter delivered my "dessert". He also arranged for cards that were signed by the duo in the Rendez-vous (who were also on our cruise 6 months prior) as well as our regular bar waiter and delivered to our table (we hang out in the Rendez-vous dancing every night usually sitting at or near the same table) as the duo dedicated a romantic song to us.