The problem with nuclear deterrents
Is that invariably they don't work if someone is crazy enough to launch a first strike.
At that point the damage is already done and there's a lot to be said for NOT retaliating.
Its actually better to concentrate on stopping the incoming missile(s) with high altitude low yield bursts which ironically have a higher chance of working than some anti-missile system while minimizing EMP damage.
IIRC the minimum yield for something like this is in the low MT range (800kt) and that will stop an incoming missile quite effectively.
AC, because this was already worked out in the 1960s and resulted in "Tsar Bomba"...