The chromosphere of cool stars is one of the least understood regions of stellar atmospheres, and modeling its structure and physics represents a fundamental challenge in stellar astrophysics. The Ca II K emission line constitutes a powerful optical diagnostic of chromospheric activity, while millimeter continuum emission provides a direct probe of the chromospheric thermal structure. Since both diagnostics form in similar atmospheric layers, their comparison provides a more complete characterization of this region. Using a homogeneous, high-S/N stellar sample obtained by TIGRE and VLT spectroscopy, we obtain precise Ca II K fluxes and widths with well-determined stellar parameters. From these uniform observations, we derive best-fit relations between Ca II K widths/fluxes and surface gravity and effective temperature, constraining how chromospheric properties scale with fundamental parameters. Long-term TIGRE monitoring (~10 yr) reveals clear links between activity level and evolutionary state, and a correlation between variability and Ca II K emission. In addition, we will present a dual diagnostic program that combines optical Ca II K with millimeter continuum emission to test new physically self-consistent PHOENIX chromospheric models that reproduce both optical and millimeter diagnostics within a unified framework. We will discuss expected correlations with gravity/temperature, links to the Wilson–Bappu framework, and how an optical-millimeter dual diagnostic program will provide unprecedented insights to answer fundamental questions about the temperature stratification, the origin of the temperature minimum, and the role of non-radiative heating mechanisms from main-sequence to evolved stars.