Measure the flight profile, estimate the mass, compare the heat signature, etc. Perhaps even radiation? Could a "Star wars" system actually gain some statistical advantage given it doesn't have the resources to shoot down every missile?
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...
But yes, best to do it before the missile debusses the warheads. Which is partly the point of GMD: yes, it's name has mid-course, but part of the point is that it pushes the point between post-boost and mid-course much closer to launch, which results in the warheads being released earlier and farther from the targets, which makes them less accurate.
Another part of BMD that isn't commonly appreciated is that Aegis/SM-3 has sufficient performance to cover about half of the US.