We demonstrate the use of a new experimental technique based on mutual inductance measurements to quantitatively predict nonlinear effects in microwave devices fabricated from high-temperature superconductor (HTS) materials. The mutual inductance measurements yield the current dependence of the penetration depth (J) in unpatterned HTS thin films. This information is used to calculate third-harmonic generation in coplanar waveguide (CPW) transmission lines and compares very well with actual measurements of CPW transmission lines of variable dimensions fabricated from YBa₂Cu₃O_7- thin film samples. The mutual inductance measurements should prove extremely valuable as a screening technique for microwave applications of HTS materials that require very low nonlinear response.