Microwave studies in the temperature range 4-300 K have been made on the different kinds of cobaltites in an attempt to observe a magnetic resonance. In a La0.9Ca0.1CoO3 single crystal a broad resonance absorption line (with g \approx 2 ) due to the presence of Co4+ ions was observed below 40 K. The measured broadening of the linewidth with decreasing temperature can be related to the process of clustering of cobalt ions. In La0.8Ca0.2CoO3 and TbBaCo2O5.5 single crystals non-resonance absorption was observed in the temperature ranges 20-90 and 240-260 K, respectively. In order to investigate the nature of this absorption its intensity was measured as a function of external magnetic field and temperature. The results could suggest that the absorption, although similar for both compounds, was caused by two different mechanisms: microwave power losses on metallic/ferromagnetic clusters in La0.8Ca0.2CoO3 and high-frequency fluctuations of the magnetic domain walls in TbBaCo2O5.5.