In uniaxial antiferromagnets (AFM), spin currents can be carried by the two eigen-modes of the systems, i.e., left- and right-handed magnon modes. Like in ferromagnets, spin currents can be generated by spin pumping and spin Seebeck effect (SSE), the former being associated with coherent magnons and the latter with incoherent magnons. I will present recent experimental studies of two uniaxial AFM materials, FeF2 and Cr2O3. FeF2 has strong uniaxial anisotropy resulting in a strong spin-flop transition field (~42 T). We have measured the spin Seebeck effect in FeF2 in magnetic fields far below the spin-flop field so that no induced magnetic moment is present at low temperatures. In addition to a low-temperature peak that is attributed to the AFM magnons, we have also observed a critical SSE peak at the AFM transition temperature. In Cr2O3, we have studied both SSE and antiferromagnetic spin pumping. We demonstrated coherently generated spin currents by 240 GHz microwave excitation and electrically detection by the inverse spin Hall effect. I will present our experimental results and analysis of the peculiar temperature dependence of the spin pumping responses in terms of coherent and incoherent magnons.