Summary: We present an experimental, analytical, and numerical investigation of the passage of electromagnetic signals through a device with voltage-dependent differential capacitance. This dependence gives rise to the device's nonlinear response, which can then be tuned by an externally applied static electric field. The system is modeled with a wave equation for the current and the charge density with continuity conditions at the boundaries between two linear regions and the nonlinear medium they sandwich. We derive asymptotic formulae for transmission and reflection coefficients of a monochromatic signal and its nonlinearity-induced second harmonics. Predictions based on this analysis are then compared with numerical and experimental results, across a range of parameter values, including those tuning the nonlinearity by means of an imposed voltage. The experiments are carried out at microwave frequencies using 1 cm\(^2\) devices consisting of a superconducting thin film meandering waveguide on a nonlinear dielectric substrate.