You can't hit what you can't see. Put an ablator on the nose of the ICBM. As it approaches burn-through the warhead salvage-fuses. Your defenders have EMP is

You can't hit what you can't see. Put an ablator on the nose of the ICBM. As it approaches burn-through the warhead salvage-fuses. Your defenders have EMP issues, but let's assume they can shield against that. The problem is now the sky is full of electronic ghosts from the first detonation. Pretty soon another warhead comes along through that ghost-filled sky. The defenders have a much harder time locating it accurately enough to fire. And, once again, when it's going to burn through it salvage-fuses. The sky gets worse. You can stop any given missile. Stopping a whole string of them is quite another matter. (Same as an aircraft pilot beating an incoming missile. Do it right and you can use the missile's speed against it, forcing it to make a turn it can't. But now you're out of position and can't do it against a second missile coming in some seconds behind.)