Equilibrium and non-equilibrium molecular dynamic simulations, predicting the dielectric properties of near critical and supercritical methanol and ethanol at microwave frequencies have been carried out. The auto correlation functions of the dielectric relaxation, show dependency on the slow component at the near-critical region for both alcohols. At the supercritical region, two competing relaxation mechanisms are observed, related to the large breakdown of the hydrogen-bonding network and the degree of clustering between the molecules. This approach closely matches experimental data at microwave frequencies and identical temperature and pressure conditions, validating the predictions of how the molecular structure and dynamics manifest themselves into the complex permittivity and dielectric relaxation behaviour. Thus, introducing a modelling-based solution to deliver accurate dielectric property values for materials at supercritical conditions for "a priori" screening of solvents, whilst removing the need to overcome engineering and safety challenges associated with the development of experimental equipment to practically generate such data.