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Princess makes it easy to know what to pack and what to wear when you're dining onboard. There are two designations for dress codes: Smart Casual and Formal. Smart Casual Evenings:
Passengers dress as they would for a fine restaurant at home.
• Skirts/dresses, slacks, and sweaters for ladies
• Pants and open-neck shirts for men
In the dining room, items such as cutoff T-shirts, shorts, halter tops, and jeans are not permitted; shoes must be worn at all times.
Just got back from a Sea Princess cruise and for the most part dress code in the Anytime Dining room was casual i.e. shirt and trousers, no jacket and tie for men and informal dress/blouse&skirt for women. On our 14 night cruise there were three formal nights that were very 'dressy' DJs black tie dark suit long dresses. If you do not want to go formal there is a buffet dining room with no dress code.