Although they are polymorphic (multiphase) materials, both copper and silver are reliable Hugoniot standards, and thus it is necessary to establish an accurate analytic model of their principal Hugoniots. Here we present analytic forms of their principal Hugoniots, as well as those of iridium and platinum, two “pusher” standards for shock-ramp experiments, over a wide range of pressures. They are based on our new analytic model of the principal Hugoniot [Burakovsky et al., J. Appl. Phys. 132, 215109 (2022)]. Comparison of the four Hugoniots with experimental and independent theoretical data (such data exist to very high pressures for both copper and silver) demonstrates excellent agreement. Hence, the new model for copper and silver can be considered as providing the corresponding Hugoniot standards over a wide pressure range. We also suggest an approach for calculating the Grüneisen parameter along the Hugoniot and apply it to copper as a prototype, and our results appear to be in good agreement with the available data.