I worked until recently in the flight test department of a major bizjet manufacturer doing this very thing. We used calculation for minor airframe alterations, and we used real flight testing for initial certification on new aircraft designs. The calculation algorithms used to get performance numbers must themselves be FAA certified, or more accurately there is an FAA-authorized rep on the company payroll called a Designated Engineering Representative (DER) doing this. But the results are gospel, and the use of calculation permits comprehensive performance documentation to be produced for any given aircraft. The older piston airplane performance numbers were approved before my time in industry and before computers in most cases, so I can't speak to that without asking around.

Great link, Ryan.