Let's be frank here. Cruise ships charge dearly for minutes on their internet. In port, you'll probably get 15 or 20 minutes online for what you pay for a single minute onboard. Yet, cruisers sit onboard while in port using the ship's pricey internet access.
As for cell phones, we got hooked for a ridiculous fee, even though the ship was in port (Long Beach). The cruise line blamed the cell phone provider, who, of course, blamed the cruise line. Turn it off or PAY UP.