We demonstrate serrodyne frequency shifting of light from 200 MHz to 1.2 GHz with an efficiency of better than 60%. The frequency shift is imparted by an electro-optic phase modulator driven by a high-frequency high-fidelity sawtooth waveform that is passively generated by a commercially available nonlinear transmission line. We also implement a push-pull configuration using two serrodyne-driven phase modulators, allowing for continuous tuning between -1.6 GHz and +1.6 GHz. Compared with competing technologies, this technique is simple and robust, and it offers the largest available tuning range in this frequency band.