The PANDA collaboration at FAIR, Germany, will focus on undiscovered charm-meson states and glueballs in antiproton annihilations to study QCD phenomena in the non-perturbative regime. For fixed target experiments at the storage ring HESR a 4π-detector for tracking, particle ID and calorimetry is under development and construction to operate at high annihilation rates up to 20 MHz. The electromagnetic calorimeters are composed of a target spectrometer (EMC) based on PbWO4 crystals and a shashlyk-type sampling calorimeter at the most forward region. The EMC, comprising more than 15,000 crystals, is operated at a temperature of −25°C and read-out via large-area avalanche photo-diodes or vacuum phototriodes/tetrodes. The photo sensor signals are continuously digitized by sampling ADCs. More than 50 of the high quality PWO-II crystals are delivered and tested. The excellent performance with respect to energy, time and position information was determined over a shower energy range from 10 MeV up to 15 GeV by operating several prototype detectors. In addition, the concept of stimulated recovery has been investigated to recover radiation damage on- and off-line during the calorimeter operation. Besides the overall concept of the target spectrometer the response function of the shashlyk spectrometer down to photon energies even below 100 MeV is presented.