My guess would be that in modern times most discoveries and breakthroughs in pure science (as opposed to technology) occur precisely this way: when observational data is sought to confirm an existing theory. The data found may indeed confirm the theory -- or may be contrary to the theory, spurring a hunt to discover what is wrong with the theory.

Examples would be the discovery of the planets Neptune and Pluto, the non-discovery of the planet Vulcan (and no, I am not talking about Star Trek), and the Michaelson-Morley experiment.