Following a critical review of related research, a method is described to evaluate the Yang–Yang critical anomaly strength function, Rμ(T), from experimental measurements of two-phase liquid and vapor isochoric heat capacities and liquid (V′) and vapor (V″) specific volumes. Direct measurements of internal energy ΔU(V,T) increments and its temperature derivative cV(T,V)=(∂U/∂T)V are made possible with a highly specialized adiabatic calorimeter. The proposed method has been applied to molecular liquids (hydrocarbons, alcohols, water, carbon dioxide, nitrogen tetroxide, etc. to accurately determine the values of the Yang–Yang anomaly strength parameter, Rμ(T=TC)=Rμ0. The calorimeter provides two-phase (liquid and vapor) isochoric heat capacities and liquid and vapor specific volumes (V″, V′) data at saturation near the critical point. These measurements have been used to evaluate the Yang–Yang anomaly strength function, Rμ(T). The values of Rμ(T)=Rμ(TC) (Yang–Yang anomaly strength parameter) derived from the calorimetric measurements for a series of fluids vary from −8 to 0.46, which is consistent with the theoretical prediction of Cerdeiriña et al. (C. A. Cerdeiriña and G. Orkoulas, M. E. Fisher, Phys. Rev. Lett., 2016, 116, 040601–040605) Near the critical point, the (T,V) variation of Rμ0 characterizes thermodynamic behavior in this region. For the first time, experimental determinations of Rμ0 have validated theoretical predictions by Cerdeiriña et al. (C. A. Cerdeiriña and G. Orkoulas, M. E. Fisher, Phys. Rev. Lett., 2016, 116, 040601–040605) that were based on the Compressible Cell Gas (CCG) model which obeys the Complete Scaling model with pressure mixing. With a valid Complete Scaling model for the physical nature and details of the temperature and the specific volume dependences of the cV2, we may now separate the measured total two-phase heat capacity into individual contributions of chemical potential cVμ and vapor pressure cVP and further, to illustrate their relative importance as a function of temperature.