The warhead(s) and decoys[1] are deployed in outer space[2]. I believe missile defense systems in this phase will use ground-based equipment like radars, and interceptors themselves use optical and other sensors to discriminate the warhead from the decoys. That said, as the linked page mentions, the decoys can have similar temperature and radar signatures as the warhead, so it's not easy. Let's not forget this is happening as these are travelling at several kilometers per second, which is no easy feat.
It's best if the missile can be disabled during the boost phase before it ever deploys the warhead and decoys.
[1] https://en.wikipedia.org/wiki/Penetration_aid [2] https://en.wikipedia.org/wiki/Ballistic_missile_flight_phase...