A good travel insurance plan (remember, not all plans are created equal) will cover you for trip delay, interruption and cancellation in the event of a major storm -- minus any compensation you get from the cruise line or airline. So if bad weather forces you to miss or reroute a flight, miss part of a cruise due to a travel delay or get stuck unexpectedly in a city overnight, you should be covered under a travel insurance plan. However, if you need to reschedule a flight and the airline has agreed to waive change fees -- or if a cruise is cut short by a day, but the line reimburses you for the missed day -- you won't get additional compensation payment.
More importantly, you will not be covered for a change of cruise itinerary. Say you booked a seven-night cruise to the Western Caribbean, but to avoid a storm, the cruise line changes the itinerary to an Eastern Caribbean one. If you're onboard for all seven nights, you will receive no compensation from your insurance provider. At best, you can hope the cruise line will take pity and throw some onboard credit your way, but don't count on it. Note: In the event that a port is canceled and replaced with another port, the line is obliged to give you nothing -- but if there's no replacement port, the cruise line will refund any port charges for missed ports in the form of onboard credit. The amount differs by line. Carnival offers a blanket amount of $20 OBC per person, per port; Royal Caribbean refunds (again, in OBC) the actual amount of the port fees, which varies by port.
Also, travel insurance covers only unexpected events. If you've neglected to pre-book insurance, your cruise departs in a week and the weatherman is suddenly reporting on an upcoming storm, don't bother calling up an insurance broker. It's too late for you to be covered. You can purchase cancel-for-any-reason policies, but these tend to be much more expensive than regular travel insurance.
Therefore we recommend that all travelers booked on a cruise during hurricane season -- who stand to suffer a sizable financial loss if the trip is delayed, interrupted or canceled -- purchase travel insurance. The best time to sign up is right before or within 24 hours after the final payment due date. That's because you're committed to going on the cruise and can't back out without penalty, but it's early enough that you'll still be covered by the insurance for unforeseen events that crop up at the last minute.
Also, a word of warning: Cruise line protection plans are technically not insurance plans, as in they are not backed by a government agency (see here for a good comparison). You will have better coverage and an outlet for help in case of a dispute with the plan provider if you book through a third-party provider. Just be sure to read all the fine print to determine what circumstances are covered and which are not before committing to any one plan.
However, ships sailing the Caribbean during hurricane season do have an out -- they can move. If a storm is threatening one area of the Caribbean or Atlantic, cruise lines will simply reroute their ships to a different destination. Passengers may still experience rough seas and may be frustrated when their Caribbean cruise turns into a Bahamas and Florida (or worse, Canada and New England) cruise, but they will be safe and won't have to suffer through the brunt of a storm.
Of course, you can also avoid hurricanes by choosing a cruise in a different part of the world, such as Alaska, Canada and New England, or the Mediterranean. Just make sure you're not moving from one hurricane zone to another. For instance, the Northeast Pacific hurricane season runs from mid-May through late November (peak in late August/early September) and can affect Mexican Riviera cruises. Asia can experience cyclones (same as hurricanes) year-round with the main hurricane season in the Northwest Pacific from July to November. Australia's cyclone season runs from late October through early May.