For the numerical solution of second order, highly oscillatory differential equations we study a class of symmetric methods that includes the St"ormer/Verlet method, the trapezoidal rule and the Numerov method. We consider Hamiltonian systems, where high oscillations are generated by a single frequency that is well separated from the lower frequencies. We apply our methods with step sizes whose product with the high frequency is in the range of linear stability, but is not assumed to be small. As a main result of this paper, we show long-time conservation of the time averages of the total energy and the oscillatory energy, and pointwise near-preservation of modified energies.