Violating liquor laws can result in severe fines, a temporary or even permanent shut down of your establishment. Laws vary from state to state so be sure to know yours. I'm most familiar with my home state of Illinois. I was serving a family once that ordered a bottle of wine for the table. It appeared to be parents and two teenaged children. They asked for four glasses. I asked to no one in particular "Is everyone at the table 21?" They replied "we're from New York, kids can have a glass of wine with their parents." That was news to me. I explained it wasn't possible here in Illinois. The following link shows 45 states allow underage drinking in various situations. Even if it might be possible in your state, check your company policy to be sure of what's acceptable to your employer.
No one wants to have the liability of underage drinking happen while they are working. You, of course, don't want to offend your patrons either. Ask and verify age with diplomacy. The example I used above asking the entire party to no one in particular "Is everyone in the party 21?" has worked for me.
Some establishments have a very strict policy of asking every single patron for an ID. While this ensures safety, it can sometimes be awkward, particularly if you have guests that are clearly well over the age of 21. Ways around offending patrons are using a little light humor or explaining the severity of the risk. If you attempt to make the patron a partner in the decision, explaining the risk, they usually understand and whip out their ID with a laugh. You can quickly glance at it and go on about the service.
Be careful when you have a table where some patrons are over 21 and others are not. Particularly if it's a crowded night there may be some sharing occurring that you want to be aware of. Again, making the patron a partner in the decision can help. You might share with them 'this is a family-owned establishment, we could lose our license." or whatever does the trick to make sure you don't have to watch them with eagle eyes while you serve your other tables.
Underage drinking on a cruise ship is more complex even still. Policies vary boat by boat and country by country. The best thing to do is understand the policy of your ship and do the best that you can to adhere to those policies.
Strange as it sounds, you should be able to 'feel' when someone is being manipulative. If you do get that feeling notify management or if you have security on staff, even better. Raising the issue to the higher level is the right and best thing to do and will ensure the issue is addressed while you continue along your busy shift!