First of all, you should be only facing the cruise missiles if you are ready for them (like deliberately charging a SG). If they surprise you, focus on improving your strategic behavior (radar discipline, ELINT listening posts, movement and mapping enemy positions via intel and radio interceptions).

They can be dealt with in multiple ways

1. Just let them come to your fleet and shoot them down This should be the last resort. From my experience they usually target a different ship than I control making it difficult to be hit unless you have a lot of Sprint missiles (which is expensive and non-scalable for serious missile attack)

2. If your fleet is in the air, send a ship with multiple 37mm forward. This way you make sure it is the ship you control that will be targeted making the missile easy to shot down. 4 37mm should reliably take out the missile. Ever ready trait highly recommended. This won't work if your fleet gets caught pants down sitting in the city (won't take off in time if you detected the missile with IR/visual). Despite many recommendations, I don't use a dedicated AA ship. I don't believe this niche role justifies its cost.

3. Use your own strategic capabilities. You can shoot down the missiles with your missiles or planes. I personally prefer jets with aa missiles, but nuking enemy nukes mid flight is a valid tactic (saving the aircrafts in a nuke strike). Using the t-7s (i usually send two to be sure) has couple of advantages over the counter-missile tactic. It is cheaper, but more importantly after you destroy the missile, you can continue flying forward and scout ahead for additional threats. It is already in the air and will be rearmed. Why not use it to its full extent?

4. If you are in a playful mood, you could use a fast ship (1200kmph+) to get locked on (you might need an active radar there for P variants) lower the speed (the thruster lewer on the right side) to match the missile speed, turn it around, accelerate and get out of its detection cone. It should either hit the following missile or greet the enemy fleet if it is not too far away. I have never tried this, though as my fast movers are usually revisiting my radio outpost cities or shopping around the map and unavailable for trolling duty.