I was only ever on one Navy ship and that was CVN 68 the USS Nimitz. However, defensive shipboard weapon systems is 100% of what I did in the Navy. The same systems I worked on are on all combat ships in the Navy. I worked on Phalanx CIWS (Close-in Weapon System), RAM (Rolling Airframe Missile) and indirectly on Evolved NATO Sea Sparrow. Links follow.
Phalanx CIWS
en.wikipedia.org
RAM
en.wikipedia.org
Evolved NATO Sea Sparrow
en.wikipedia.org
I was much younger then and I honestly ached for someone to try to fire a missile at my ship so that we could shoot it down and be heroes. I realize now how dumb that was, regardless, I had an extreme amount of confidence in myself and the people I worked with. Our division had just over 20 people in it but my work center, which was responsible for the RAM systems, had 6-8 people at any given time. I was the work center supervisor, or the POIC (petty officer in charge) of the RAM work center for most of my time on the ship. Before I was the POIC my battle station was at the RAM console in CIC (Combat Information Center) which meant I was the guy that would push the "fire" button to engage a target that was threatening my ship.
In my humble opinion you would have to fire either a concentrated stream raid of guided missiles (look stream raid up) or a couple of hypersonic missiles in order to hit my ship. I was directly involved in testing our defensive capability against hypersonic missiles and I hope we have improved our ability to counter them. As it stands I think the primary defensive measure is distance.
A few missiles fired at my ship, good luck some other time, that **** isn't going to work.
Keep in mind also that I worked on point defense weapon systems. The cruisers and destroyers have AEGIS systems and standard missiles that can engage MUCH further out than the stuff I worked on. Also consider that Navy aircraft is the actual first line of defense for a Navy strike group. So you would have had to peel the onion back pretty far before I would have been needed.
The U.S. Navy isn't a joke. There aren't 5 other navies combined that could even think about messing with the U.S. Navy and at least two of those are very close allies, and they are 2 and 3 on the list.