Context. The energetics and physical conditions of the interstellar medium and feedback processes remain challenging to probe.Aims. Shocks, modelled over a broad range of parameters, are used to construct a new tool to deduce the mechanical energy and physical conditions from observed atomic or molecular emission lines.Methods. We compute magnetised, molecular shock models with velocities Vs = 5–80 km s−1, pre-shock proton densities nH = 102–106 cm−3, weak or moderate magnetic field strengths, and in the absence or presence of an external UV radiation field. These parameters represent the broadest published range of physical conditions for molecular shocks. As a key shock tracer, we focus on the production of CH+ and post-process the radiative transfer of its rovibrational lines. We develop a simple emission model of an ensemble of shocks for connecting any observed emission lines to the mechanical energy and physical conditions of the system.Results. For this range of parameters, we find the full diversity (C-, C*-, CJ-, and J-type) of magnetohydrodynamic shocks. H2 and H are dominant coolants, with up to 30% of the shock kinetic flux escaping in Lyα photons. The reformation of molecules in the cooling tail means H2 is even a good tracer of dissociative shocks and shocks that were initially fully atomic. The known shock tracer CH+ can also be a significant coolant, reprocessing up to 1% of the kinetic flux. Its production and excitation is intimately linked to the presence of H2 and C+. For each shock model we provide integrated intensities of rovibrational lines of H2, CO, and CH+, and atomic H lines, and atomic fine-structure and metastable lines. We demonstrate how to use these shock models to deduce the mechanical energy and physical conditions of extragalactic environments. As a template example, we interpret the CH+(1−0) emission from the Eyelash starburst galaxy. A mechanical energy injection rate of at least 1011 L⊙ into molecular shocks is required to reproduce the observed line. We find that shocks with velocities as low as 5 km s−1 irradiated by a strong UV field are compatible with the available energy budget. The low-velocity, externally irradiated shocks are at least an order magnitude more efficient than the most efficient shocks with no external irradiation in terms of the total mechanical energy required. We predict differences of more than two orders of magnitude in the intensities of the pure rotational lines of CO, Lyα, and the metastable lines of O, S+, and N between representative models of low-velocity (Vs ~ 10 km s−1) externally irradiated shocks and higher-velocity shocks (Vs ≥ 50 km s−1) with no external irradiation.Conclusions. Shock modelling over an extensive range of physical conditions allows for the interpretation of challenging observations of broad line emission from distant galaxies. Our new method opens up a promising avenue to quantitatively probe the physical conditions and mechanical energy of galaxy-scale gas flows.