The Smithsonian has a really cool article on modern day pirate huntersat www.smithsonion.com.

Pirate attacks are on the rise, and today's pirate hunters use high tech weapons--like a guided-missile destroyer USS Winston S. Churchill!

In pursuit of the hijacked dhow, the Churchill had the advantage of surprise. The pirates "couldn't see us over the horizon" during the night, the ship's executive officer, Lt. Cmdr. Erik Nilsson, told me in a telephone interview. But at first light the destroyer deliberately showed itself to the crew of the dhow, and the pirates took off to the west. Somalia's territorial waters—from which the Churchill was barred by international law—were 80 nautical miles away.

But, it can still take a while before these modern ships can catch up to modern-day pirates:

"We repeatedly radioed and asked [the dhow] to halt," [Captain] Nilsson said. When the pirates refused, the U.S. sailors called to them over an amplified megaphone, without effect. The chase went on all morning and into the afternoon. With Somali waters only four hours away, the Churchill closed to within 500 yards of the dhow and fired across its bow with its 25-millimeter chain guns. "That got the pirates' attention, and they stopped," Nilsson said.