How do I avoid problems logging in to my Hotmail account from a cruise ship?

Sorry to hear that you’re worried about this. There is no setting that can guarantee your Hotmail/Outlook.com account will not ask for verification while you are using cruise ship Wi-Fi, because Microsoft may request a security check when you sign in from a new location, network, or device.

Before you travel, I recommend signing in successfully from your laptop while you are still at home, then review your Microsoft account security info and make sure you have recovery options you can actually access during the cruise, such as an alternate email or Microsoft Authenticator app. Microsoft also recommends keeping multiple security contact methods on the account, especially if two-step verification is enabled.

https://account.live.com/proofs/manage/additional

Also, from the laptop you will take with you, sign in to your Microsoft account security settings and, when prompted, choose the option that says keep you signed. This can make the laptop a trusted device, although it still does not override all security checks.

During the trip, avoid signing out, clearing browser cookies, and using private/incognito browsing. If possible, keep the Outlook app or Outlook.com already signed in before boarding. Also, make sure your phone can receive verification codes, or use the Authenticator app if SMS may not work on the ship.

If the account is still blocked or challenged, you will need to follow the sign-in screen instructions or use Microsoft’s Sign-in Helper.