The biggest weakness of the sunburn is it's range 200, miles and a flight time of under three minutes. For the sunburn to be a threat, the attacking ship needs to get within range. This is going to be very hard to do. The maximum range of U.S. Navy strike aircraft is considerably longer than 200 miles. Good luck getting past the F-18 super hornets. But lets say they did.
There is the (SM-2) missile, which has a range of 74 to 166 kilometers.
The second system is the Evolved Sea Sparrow (ESSM), which is used in packs of four that fit into one cell of the Mk 41 vertical-launch system. This system has a range of over 15 kilometers.
Then Rolling Airframe Missile (RAM) is a variation of the venerable AIM-9 Sidewinder. This system, in a 21-round launcher, and has a range of nine kilometers.
And if all of those fail we have the Phalanx Close-in-Weapon-System (CIWS). This is a 20-millimeter Gatling gun firing depleted uranium or tungsten rounds at 3,000 - 4,500 rounds per minute to destroy the missile before it hits the ship.
They have a good weapon but were not crippled, we are in good hands.