The Calar Alto Secondary Eclipse study was a program dedicated to observe secondary eclipses in the near-IR of two known close-orbiting exoplanets around K-dwarfs: WASP-10b and Qatar-1b. Such observations reveal hints on the orbital configuration of the system and on the thermal emission of the exoplanet, which allows the study of the brightness temperature of its atmosphere. The observations were performed at the Calar Alto Observatory (Spain). We used the OMEGA2000 instrument (Ks band) at the 3.5m telescope. The data was acquired with the telescope strongly defocused. The differential light curve was corrected from systematic effects using the Principal Component Analysis (PCA) technique. The final light curve was fitted using an occultation model to find the eclipse depth and a possible phase shift by performing a MCMC analysis. The observations have revealed a secondary eclipse of WASP-10b with depth of 0.137%, and a depth of 0.196% for Qatar-1b. The observed phase offset from expected mid-eclipse was of -0.0028 for WASP-10b, and of -0.0079 for Qatar-1b. These measured offsets led to a value for vertical bar e cos omega vertical bar of 0.0044 for the WASP-10b system, leading to a derived eccentricity which was too small to be of any significance. For Qatar-1b, we have derived a vertical bar e cos omega vertical bar of 0.0123, however, this last result needs to be confirmed with more data. The estimated Ks-band brightness temperatures are of 1647 K and 1885 K for WASP-10b and Qatar-1b, respectively. We also found an empirical correlation between the log(R'(HK)) activity index of planet hosts and the Ks-band brightness temperature of exoplanets, considering a small number of systems.