It turns out that American “super carriers” are more resistant to combat damage than most people think. Because of their size (100,000 tons) it's been possible to protect these ships much better than potential foes realize. Many in the U.S. Navy carrier community believe these large ships are actually more resistant to modern anti-ship missiles, including those with shaped charge warheads, than the 45,000 ton Iowa class battleships. These were the pinnacle of battleship design, entering service in 1943 and only removed from the reserve (of older ships kept around just in case) in the last decade. The Iowa class ships served in Vietnam and the Gulf War. In both conflicts they made themselves useful with their 16 inch (406mm) guns, delivering one ton shells in support of American ground troops.
Carrier experts in the navy have been gradually modifying the design and protection of the large carriers for decades, taking into account what new generations of large anti-ship missiles (“carrier killers”) could do. These design tweaks and damage control measures have been kept quiet, and often secret, to deny the anti-ship missile developers knowledge that they can use to improve their designs.
The U.S. Navy has also used old ships for target practice to see just how well these design changes perform in realistic conditions. For example, most of the 30 decommissioned Spruance class destroyers were used for this kind of target practice. Running a SINKEX (sinking exercise) enables the navy to test some theories on how vulnerable, or invulnerable, modern warships are. Carriers are rarely employed for this but a 1996 SINKEX was conducted using the retired 82,000 ton carrier USS America. This classified exercise was a test of the vulnerability of such large ships to modern anti-ship missiles. While the exercise details were secret, it did get out that carriers this size were very hard to sink.