The zero bias tunneling conductance is investigated theoretically and shown to be a promising experimental tool for detecting first order phase transitions in high field superconductors. We calculate and evaluate numerically the zero bias tunneling conductance for arbitrary spin orbital mean free path. In doing the calculations we distinguish between thin films in a parallel field and highℵ-value materials in a perpendicular field. In the former case anomalous properties appear for sufficient long spin orbital mean free path. Finally we determine the minimum spin orbital mean free path which is compatible with a first order phase transition and show that it is much smaller than commonly believed.