I'm not that familiar with the literature. The only thing that comes to mind is Einstein's thought experiment, involving an observer on a rapidly rotating disk. His measuring rod remains unchanged as he moves out from the center along a radial line (he keeps the rod pointing toward the center), but when he's at the circumfrence (which is spinning rapidly) and he rotates his rod and begins to measure the circumfrence, his rod is shortened by the disk's acceleration, and he discovers that he has measured out a longer circumfrence than the radius would have indicated. But I know of no actual experimental evidence. That would require a very strong disk to withstand such rapid motion -- and you thought your hard drive was high tech.
Michelson-Morely is how we can measure Lorentz contraction. Three things have to come into play to produce a null result in that experiment: the finite speed of light, time dilation, and Lorentz contraction. Now that we can independently measure the first two to a high degree of accuracy, we can take the MM experiment as a test of Lorentz contraction. As predicted by relativity, it is exactly as much as it needs to be to cancel the influence of the first two effects on the interferometer.