We demonstrate serrodyne frequency shifting of light from $200\mathrm{MHz}\text{to}1.2\mathrm{GHz}$ 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 $-1.6\mathrm{GHz}$ and $+1.6\mathrm{GHz}$ . Compared with competing technologies, this technique is simple and robust, and it offers the largest available tuning range in this frequency band.