I've noticed that no one has yet come up with the obvious solution. Warships of any normal kind are impractical. There's too much area to cover, they're too limited in visibility, and they're too slow to cope with the smaller, faster, more maneuverable pirates. Convoys increase the expense, and decrease the shipping speed.
An article I read earlier this week had a good solution. Helicopter ships. Armed helicopter gunships on a dedicated platform. Can cover more area in less time, greater visibility, and greater ability to deal with the small speedboat craft. Set up several platform ships in a chain, and you can cover an immense area compared to a similar number of traditional warships; and your response time is greatly improved.
It's not a cheap solution, or a perfect one; but it's workable and effective.
Luchog, most modern combatants have on board helicopters, so your suggestion, while not bad, is redundant in the sense that ship borne helicopters are already there. US has armed it's ship borne helos since the mid 1990s, most NATO nations before that. Ships with organic helos have a surveillance range many times that of a ship with no helo, which is why we've had helos on surface combatants -- frigates, destroyers, cruisers -- since the mid 1970's.
Another thing we (the US) now have on a variety of ships is UAV's, which can help a lot with the maritime surveillance package.
Also, in that part of the world, more than one NATO nation deploys (or has deployed) multi enging maritime patrol planes, with long on station times, like the Argus, Nimrod, Orion, or even Atlantique. (Not sure if Atlantique's are still deployed there. )
Sum up: what you are looking for is already there, or easily put there.
(Ya sorta threw that pitch into my wheelhouse.

)
@ toke: a 25mm chain gun ought to suffice for your ship. Mount one on each bridge wing. We had them welded to our ships' main decks after the lessons learned in Praying Mantis/Earnest Will in the late 1980's, in terms of getting a mid sized gun for a small sized boghammer or such like craft.
@ Joey Donuts: were you on
Barry when CDR Balconis was the CO?
DR