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A dinner suit or a normal business suit will be fine. Ladies should be in a floaty evening dress. If you do not wish to partake then you just go and eat in the buffet area.
On most Royal Caribbean ships most of the dinner menu is often available in your cabin.
You will also find that often when the dress code is formal for the main restaurant the dress code in the specialty restaurants is smart casual.
The daily on board news sheet will give you all the information you need.