Positron emission tomography (PET) system energy response is typically characterized in singles detection mode, yet there are situations in which the energy spectrum of coincidence events might be different than the spectrum measured in singles mode. Examples include imaging with isotopes that emit a prompt gamma in coincidence with a positron emission, imaging with low activity in a LSO/LYSO-based cameras, in which the intrinsic activity is significant, and in high scatter situations where the two 511 keV photons have different scattering probabilities (i.e. off-center line source). The ability to accurately measure the energy spectrum of coincidence events could be used for validating simulation models, optimizing energy discriminator levels and examining scatter models and corrections. For many PET systems operating in coincidence mode, the only method available for estimating the energy spectrum is to step the lower and upper level discriminators (LLD and ULD). Simple measurement techniques such as using a narrow sliding energy window or stepping only the LLD will not yield a spectrum of coincidence events that is accurate for cases where there are different energy components contributing to the spectrum. In this work we propose a new method of measuring the energy spectrum of coincidence events in PET based on a linear combination of two sets of coincident count measurements: one made by stepping the LLD and one made by stepping the ULD. The method was tested using both Monte Carlo simulations of a Siemens microPET R4 camera and measured data acquired on a Siemens Inveon PET camera. The results show that our energy spectrum calculation method accurately measures the coincident energy spectra for cases including the beta/gamma spectrum of the (176)Lu intrinsic activity present in the LSO scintillator crystals, a (68)Ge source and an (124)I source (in which there are prompt gamma-rays emitted together with the positron).