The performance of electromagnetic calorimeter modules made of proton-irradiated PbWO4 crystals has been studied in beam tests. The modules, similar to those used in the Endcaps of the CMS electromagnetic calorimeter (ECAL), were formed from 5×5 matrices of PbWO4 crystals, which had previously been exposed to 24 GeV protons up to integrated fluences between 2.1× 1013 and 1.3× 1014 cm−2. These correspond to the predicted charged-hadron fluences in the ECAL Endcaps at pseudorapidity η = 2.6 after about 500 fb−1 and 3000 fb−1 respectively, corresponding to the end of the LHC and High Luminosity LHC operation periods. The irradiated crystals have a lower light transmission for wavelengths corresponding to the scintillation light, and a correspondingly reduced light output. A comparison with four crystals irradiated in situ in CMS showed no significant rate dependence of hadron-induced damage. A degradation of the energy resolution and a non-linear response to electron showers are observed in damaged crystals. Direct measurements of the light output from the crystals show the amplitude decreasing and pulse becoming faster as the fluence increases. The latter is interpreted, through comparison with simulation, as a side-effect of the degradation in light transmission. The experimental results obtained can be used to estimate the long term performance of the CMS ECAL.