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Missiles move very fast.

But they don't change course that fast. They have great velocity, but only average acceleration. These copters have really good acceleration at low speeds, so they should be able to get in the way of a missile with a known target really well.

not really necessary... http://en.wikipedia.org/wiki/Close-in_weapon_system

Use the quadroptors in depth: first is furthest out to force a missile course change, next several sit behind and flanking first on the likeliest course changes. Integrate these with the CIWS to define "holes" where the gun can expect to find the missile.

Or, make a big one, station it up and miles off, and have it launch heat + radar homing counter missiles, timed to intercept incoming with "matching" intercepts rather than "crossing" intercepts.

Sorry about the late reply. That's a creative idea. At first blush a defense of these seems equivalent in the sense that both are somewhat "stochastic" defense mechanisms - throw up a wall of obstructions and hope something collides.

Send two or three missiles in a row.

The Russian P-700 Granit anti-ship missile can operate in a networked swarm:

http://en.wikipedia.org/wiki/P-700_Granit