Does the US not have a supersonic SSM?

[SandyCaesar]

Aegis, plus the Russian S-300 cruisers, the Slavas and Kirovs. Maybe the SA-N-9 equipped ships, too, Neustrashimy and Udaloy classes. From what I've heard, the Gauntlet is a scary little missile at short ranges, and combined with the Kashtan rotary-30mm/SA-N-11 system I'd rate it as a pretty good point-defense weapon.

Aside from that, I'm not sure. The PAAMS missile, Aster 15 and 30, seem to be the European counterparts, but as far as I know they're not yet in active service.

So apart from Aegis, the Russian S-300/SA-N-6 (and maybe the SA-N-9, but its short range precludes defense against big swarms), and the future PAAMS, I don't know of any real anti-swarm weapons. ESSM has the range and the ability to do it, but it requires a powerful radar system, like the Aegis, to engage swarms effectively. Other systems, like Crotale, Sea Sparrow (RIM-7, not RIM-161), or Sea Wolf, are point-defense weapons that probably can't handle SSM swarms very well.