We report on high-field electron spin resonance studies of two iridium hexahalide compounds (NH4)2IrCl6 and K2IrCl6. In the paramagnetic state, our measurements reveal isotropic g factors g=1.79(1) for the Ir4+ ions, in agreement with their cubic symmetries. Most importantly, in the magnetically ordered state, we observe two magnon modes with zero-field gaps of 11.3 and 14.2 K for (NH4)2IrCl6 and K2IrCl6, respectively. Based on that and using linear spin-wave theory, we estimate the nearest-neighbor exchange couplings and anisotropic Kitaev interactions J1/kB=10.3K, K/kB=0.7K for (NH4)2IrCl6, and J1/kB=13.8K, K/kB=0.9K for K2IrCl6, revealing the nearest-neighbor Heisenberg coupling as the leading interaction term, with only a weak Kitaev anisotropy.