Found an article about a New York art dealer that seems to have been suckering people for quite a while with a pretty clever scheme. He's been arrested by the FBI, which has been investigating him for years, impeded by the fact that since the paintings have moved around the world in both Europe and Asia as well as in the US, the case has been difficult to put together. Here's the short version of what he does.
He buys a valuable painting, but one that isn't really high class. Not worth millions, but a few hundred thousand. Has it copied and then sells the copy with the certificate of authenticity from the original and then the original without the certificate of authenticity. Since the original is the real McCoy, no big deal. And though it's a risk to sell both original and copy, since he's sold both paintings, by the time the fraud is discovered, both paintings have usually changed hands a couple times. There are some other details that helped his scheme to run smoothly, but suffice it to say that he was a very clever guy.