We present a comprehensive study of broadband (0–2 GHz) electrodynamic properties of coplanar waveguides made from high-temperature superconducting thin-film YBa ₂ Cu ₃ O _7-δ electrodes on nonlinear dielectric single-crystal SrTiO ₃ substrates. The waveguides exhibit strong dielectric nonlinearities, in addition to temperature-, dc-bias-, and frequency-dependent dissipation and refractive index. By using parameters determined from small-signal (linear) transmission characteristics of the waveguides as a function of dc bias, we develop a model equation that successfully predicts and describes large-signal (nonlinear) behavior. © 1999 American Institute of Physics.