Marcus Antonius the Orator, grand-father of Mark Anthony, fought the pirates and was awarded a Triumph over them in 99 BC. One of Marius' relations lost his life there, but for the life of me I can't remember which one ....
There is a famous Pirate Law inscribed on the Monument of Aemilius Paullus in Delphi, which includes the name of Gaius Marius as consul. It dates to 100 BC, is fragmentary, and in all the early books and articles is seen as an attempt by Marius to gain an Eastern Command; today this view is no longer credited, and it is associated with Antonius' campaign.
My favorite Roman pirate story is that of Julius Caesar - they captured and ransomed him. Then he went back, and crucified them. See Caesar and the pirates, and Plutarch, Caesar, 2:
He went to Pergamon, took the pirates out of prison and crucified the lot of them, just as he had often told them he would do when he was on the island and they imagined that he was joking.
For more about Rome and Pirates Livius has a great summary.