We report on a detailed study of the X-ray spectrum of the nearby eclipsing spectroscopic binary YY Gem. Observations were obtained simultaneously with both large X-ray observatories, XMM-Newton and Chandra. We compare the high-resolution spectra acquired with the Reflection Grating Spectrometer onboard XMM-Newton and with the Low Energy Transmission Grating Spectrometer onboard Chandra, and evidence in direct comparison the good performance of both instruments in terms of wavelength and flux calibration. The strongest lines in the X-ray spectrum of YY Gem are from oxygen. Oxygen line ratios indicate the presence of a low-temperature component (1-4 MK) with density n_e < 2 10^{10} cm^-3. The X-ray lightcurve reveals two flares and a dip corresponding to the secondary eclipse. An increase of the density during phases of high activity is suggested from time-resolved spectroscopy. Time-resolved global fitting of the European Photon Imaging Camera CCD spectrum traces the evolution of temperature and emission measure during the flares. These medium-resolution spectra show that temperatures > 10^7 K are relevant in the corona of YY Gem although not as dominant as the lower temperatures represented by the strongest lines in the high-resolution spectrum. Magnetic loops with length on the order of 10^9 cm, i.e., about 5 % of the radius of each star, are inferred from a comparison with a one-dimensional hydrodynamic model. This suggests that the flares did not erupt in the (presumably more extended) inter-binary magnetosphere but are related to one of the components of the binary.