What does a normal emg/nerve conduction test tell you?

No pinched nerves: A normal test would tell you that the nerves tested are not pinched or slow. The normal EMG (the needle part of the test) would tell you that the muscle are not showing signs of damage (to either the muscle itself or the nerves).

Interpretation: Assuming the test was comprehensive and technically competent, this can eliminate large fiber neuropathy, and most muscle diseases. But does not eliminate small fibre neuropathy, or disease of brain and/or spinal cord. Symptoms due to intermittent nerve compression are not fully excluded either.