An electro-optic modulator imparts the information contained in an electrical signal traveling along a transmission line onto an optical carrier by using signal-related variations in the electrical signal's voltage to modulate the refractive index or absorption in an electro-optic material through which the optical carrier propagates. For optimal bandwidth and modulation efficiency, the microwave and optical waves should be matched in velocity. However, conventional microwave transmission lines have a microwave velocity that is somewhat higher than the optical group velocity in typical optical waveguides. Tuning a microwave transmission line's capacitance reduces the microwave velocity, but also reduces the impedance below the 50Ω impedance of most microwave components. Conversely, tuning the microwave transmission line's inductance makes it possible to match the microwave velocity to the optical group velocity over bandwidths of 100 GHz or greater while maintaining a microwave impedance of 50Ω.