Actually, the precession of the perihelion of Mercury was known before GR. (I'll assume you meant GR, as SR isn't enough to predict that quantity.) While the correct calculation was an early success of GR, it doesn't really count as an experimental test, as the result was known before the calculation. The most important early experimental test was Eddington's precision measurement of the abberation of starlight by the sun.
As for SR, there are numerous experimental tests. There are no experimental results that disagree with either SR or GR.
From: Bill Walker <walker@ifm.mavt.ethz.ch> Date: Fri, 27 Jun 1997 16:29:59 +0200 (69kb) Date (revised): Mon, 28 Jul 1997 20:37:18 +0200
The near-field Lienard-Wiechert potential solution of a longitudinally oscillating electrical field produced by an oscillating charge is presented, and the results are compared to the R. P. Feynman multipole far-field solution. The results indicate that the phase speed of a longitudinally oscillating electrical field is much faster than the speed of light in the near field.