Royal Caribbean recently changed their boarding window to 90 minutes, meaning you'll have to be checked in and actually onboard the ship by 3:30.
Here are a few things you can do if you don't change your flights. First, make sure you have travel insurance that will cover you for any type of flight delay. Read the fine print to make sure your airline is covered. (Actually, insurance is a must-have, anyway, as you never know what can happen to interrupt your cruise.) Now, insurance won't make them hold the ship, but it will help cover costs you incur as a result of the delay. Second, you can check in online through Royal Caribbean's Web site. This can be done at any time UP TO three days before the cruise. This will shave a few minutes off of the boarding process at the pier. Note that you will still have to show your IDs when checking in, so be sure to have those handy, and not in your checked luggage.