Maybe to shoot down airliners that had been hijacked ? I am sure there are many reasons having to do with defending an attack on a coastal city.
And how would it work?
I could give you all kinds of guesses, but the truth is I don't know. But... then I don't know exactly how most military grade missile tracking systems work. I could probably list the various types if you want. The differences seem to be in what is used for targeting, how accurate that is, and when and how any 'explosive charge' is released.
I admit I can't think of any. Why would you shoot down hijacked airliners? Why wouldn't you use aircraft to intercept them?