The paper presents the results of studies of the influence of cobalt on the structure and mechanical properties of kovar (29НК)–stainless steel (12X18H10) brazed dissimilar joints obtained by vacuum brazing using brazing filler metal of the Cu–Mn–Co system. Micro X-ray spectral studies of brazed dissimilar joints prove that a structure of a solid solution based on copper is formed in brazed joints, which contains a small amount of discrete grains of the $\gamma$-phase (solid solution based on Fe–Mn–Co). An increase in the concentration of cobalt in the initial brazing filler metal from 0.5 to 4.5% wt. leads to a slight increase in its concentration in a solid solution based on copper and a significant increase in its concentration in discrete grains of the $\gamma$-phase—from 8.44 to 19.7% mass. Such structural features of brazed joints positively affect their mechanical properties and contribute to an increase in the shear strength of kovar–stainless steel brazed overlap dissimilar joints from 374 to 434 MPa.