A few examples I can think of off the top of my head, to give a feel for the reference class I'm looking for:

- The existence and position of Neptune were predicted from observations of Uranus's orbit, before anyone had ever observed Neptune directly

- Black holes were predicted from the equations of General Relativity before we'd ever observed them or their effects on stars' motion

- Not as quantitative, but Darwin's theory of Evolution predicted that we'd find some method by which natural selection actually occurs, before we ever knew about DNA.

Are there other cool examples like these?

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Einstein predicted the bending of light around the sun based on general relativity in 1915. In 1919 it was confirmed with a famous expedition and observation of an eclipse by Eddington. https://en.wikipedia.org/wiki/Tests_of_general_relativity

Newton's equations predict that objects fall at the same rate in the absence of atmosphere. Confirmed experimentally on Earth once vaccum chambers were constructive, and dramatically on the moon with a feather and hammer https://youtu.be/KDp1tiUsZw8

Experiments with falling objects, from the time of Galileo onwards, demonstrated that objects of differing weight, but the same shape and density, did indeed fall at about the same rate.  Also objects of the same weight, but differing shapes and/or densities fell at different rates; thus strongly supporting the hypothesis that the differences in rates of falling were due solely to air resistance.  The later experiments, conducted in vacuum, simply confirmed beyond reasonable doubt this hypothesis.

That's one of my favorite demonstrations! It was easy enough to know that this is true, but seeing it with one's own eyes is shocking, or at least was for me.

Along with your black hole example and Jeff's light bending example, Relativity also predicted time dilation and gravitational waves before they were confirmed experimentally.

I remember reading about Higgs in the news a couple of year ago. It was a very fascinating discovery.

"It has not escaped our notice that the specific pairing we have postulated immediately suggests a possible copying mechanism for the genetic material." 

In their 1953 DNA helix paper, Watson and Crick  also predicted that DNA would replicate in a semiconservative manner. This was later confirmed to be true in Meselson's and Stahl's experiment  in 1958.