In a Traveller setting, at least, given that we're assuming ships are able to exchange missile and torpedo fire whilst moving at (potentially) several Km/s relative to one another, even against wildly evading small craft, I think anti-missile fire is believable with a suitably specialised round.
Essentially, you'd probably just stick a sandcaster barrel of sand or pebbles (or something essentially resembling one) in place of a normal warhead.
Even a fairly light strike is essentially lethal - a missile can't be armoured enough to shrug off a high-velocity impact, even a small one, without being slow and unmanouvrable enough to be dead meat for pulse/beam laser fire from more conventional point defences.
Given the almost obsessive interoperability of 3I technology, you could probably get away with firing it through a conventional missile launcher, firing it at the incoming salvo.
Working on the assumption that it's more or less the same as a normal missile aside from the warhead and fusing, time to impact would logically be half the remaining time to impact of the salvo (unless we want to get into simultaneous UVAST equations. In which case don't call us, we'll call you). Launching them is a reaction, but one that doesn't have to wait until turn-of-impact, giving you a better chance of thinning out an incoming barrage before it all goes to fleeble.
That just leaves the question of what the difficulty roll should be.
The gunnery check effect defining the missile 'to hit' roll remains sensible, but the shot will unarguably be more difficult than trying to hit a starship under equivalent circumstances, so I would assign the missile a number of levels of 'automatic dodge' (i.e. some multiple of -2 DM on the counter-missile's to hit roll).
Two levels, giving a -4 DM, so that the gunnery check has to be at least a basic success to give any chance to the counter-missiles, seems a fair-for-gaming if not scientifically justifiable fudge. If you want to be picky you might increase that slightly for missiles or decrease it for torpedoes, as the torpedo is thirty times larger, which surely must make for an easier target as there's no indication it travels faster (same flight time).
I mean that in the nicest way. I believe they believed if they spent enough money they would solve any problem. Where "enough" is more than exists in some cases but when you're just taking it a billion here and a billion there nobody says much 
