It should be simple.
Death to Pirates.
You find them, you kill them. You blow they vessels out of the water or strafe them with .50 caliber machine guns and/or 40mm grenade fire. You set their shore facilities ablaze. You release the video of their destruction on YouTube in two version: straight destruction version, and a mocking-commentary-with-funny-music version (think Mystery Science theater or American Pro Football commentary with music alternating between American rock ‘n’ roll that Benny Hill music). If their activity increases you use USGOV (and friendly allies) Air and Navy power to patrol and seek out the Pirates. You put Marines and Seals and armed Coasties and private security forces on commercial vessels to provide discreet security and lay counter ambushes. You use UAVs and Airships for surveillance. You buy up some old dredge ships and send them in as bait filled with Coasties, Marines, and Seals. Armed UAV should being fire missiles at their vessels. You use a couple of small diesel submarine firing cost-effective (small blast) guided torpedoes to take them out and to shadow friendly shipping. Nobody who matters cares when Pirates are killed. Mock and ignore anybody who does. Heck practice some anti-pirate lawfare: sue the supporters and appeasers of pirates and seize their assets in the financial system. Drop leaflets over pirate friendly neighborhoods mocking the pirates and listing the current kill totals.
The aim is to reduce the current profit and the expected future profit of being a pirate – both Economic and Social. The goal is to stop piracy.
It really is simple.
The Royal Navy and Marines just killed two pirates and stopped a piracy attempt. Good on them. More please. And release the video.
Death to Pirates.