Next-generation millimeter-wave $(g30\phantom{\rule{0.1em}{0ex}}\mathrm{GHz})$ telecommunications electronics must be compact, energy efficient, and have good thermal management. Tunable materials may play a role in meeting these requirements for millimeter-wave front-end devices, but there are few models or even measurements of tunable dielectrics at these frequencies. Here, we report on the adaptation and development of high-frequency dielectric spectroscopy techniques for composition-spread thin films from 100 MHz to 110 GHz. Our comprehensive technique sequentially probes the composition, frequency, and electric field dependence of the complex permittivity in a combinatorial thin film library, which provides a platform to rapidly explore functional materials for emerging telecommunications electronics. This is achieved by modifying existing on-wafer transmission line permittivity measurement techniques to obtain a compact set of test devices that can be patterned to extract the complex permittivity in multiple regions of a thin film. We demonstrate this technique by applying it to composition-spread ${\mathrm{Ba}}_{1\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{Ti}\mathrm{O}}_{3}$ thin films spanning compositions from $x=0$ to $x=1.$ The systematic approach to materials growth inherent in combinatorial synthesis allows for a comprehensive picture of the ${\mathrm{Ba}}_{1\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{Ti}\mathrm{O}}_{3}$ system. Our continuous, quantitative measurements provide an encompassing view of the composition- and voltage-dependent trends in the room temperature dielectric properties at millimeter-wave frequencies---from strong, few-picosecond relaxations to no relaxation, and from large relative tunability (${n}_{r}g50\mathrm{%}$ at $75\phantom{\rule{0.1em}{0ex}}\mathrm{k}{\mathrm{V}}_{}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}1}$) to zero tunability. Our work underscores both the utility of our technique, and the need to discover lower-loss, highly tunable electronic materials for next-generation telecommunications.
