There are effects that come out of the math of the frame dragging theory. Scientists are currently testing one which is that if one small spinning object is orbiting a larger spinning object, the smaller object will slowly adjust its spin axis (the imaginary line which an object rotates around) to align with the larger object's spin axis. This is known as the Lense-Thirring effect. They are testing this theory by having a gyroscope (an object that will normally keep its spin axis the same) orbit the Earth, and testing whether its spin axis will align with the Earth's spin axis. So far, scientist say that they have evidence that proves the Lense-Thirring effect (and possibly the frame dragging theory) to less than .5% accuracy.