The microwave dielectric loss of stoichiometric and non-stoichiometric Ba(Co1/3Nb2/3)O-3 ceramics have been measured from 2 to 300K in magnetic fields ranging from 0 to 5T using a dielectric resonator (DR) technique. The microwave absorption from spin excitations of unpaired d-electrons in exchange coupled Co2+ ions dominate the loss of the Ba(Co1/3Nb2/3)O-3 ceramics at cryogenic temperatures. Two peaks in the loss tangent (tan ) vs temperature relation from a distinctly different origin occur at 25-30K and 90K, which increase in magnitude with increasing Co content in the bulk dielectric samples. Evidence that these peaks result from polaron conduction from hopping between Co2+ and Co3+ ions includes (i) the peak's observed temperature range; (ii) the decrease in peak intensity of approximately a factor of two in a large applied magnetic fields (5T); and (iii) a strong correlation between the peak's magnitude and both the fraction of the minority Co3+ in the dominant Co2+ matrix and D.C. conductivity at elevated temperatures. A magnetic-field independent high temperature peak with a maximum at 250K dominates the room temperature microwave loss whose magnitude correlates with those of the low temperature peaks. This suggests that the defects responsible for carrier conduction play an important role in establishing the loss tangent at room temperature.