We study the evolution of the maximum energy E-max(t) reached between time 0 and time t in the dynamics of simple models with glassy energy landscapes, after an instant quench from infinite temperature to a target temperature T. Through a detailed description of the activated dynamics, we are able to describe the evolution of E-max(t) from short times, through the aging regime, until after equilibrium is reached, thus providing a detailed description of the long-time dynamics. Finally, we compare our findings with numerical simulations of the p-spin glass and show how the maximum energy record can be used to identify the threshold energy in this model.