Phase equilibria in the Ag-Co and Ag-Ni-Co systems were experimentally determined. Thermodynamic assessments for these two systems were performed by applying the Calculation of Phase Diagrams method on the basis of the present and previous experimental results. The optimized thermodynamic parameters bring about a good agreement between the calculated results and experimental data in these two systems. Solidification experiments were conducted for Ag-Ni-Co alloys, and samples with composite microstructure were obtained, in which the (Ni, Co)-rich dispersed-phase particles (DPPs) distribute uniformly in the Ag matrix. The microhardness of the Ag-Ni-Co alloys increases with the content of nickel and cobalt and the cooling rate of the alloys during solidification. A model was developed to analyze the solidification microstructure formation of Ag-Ni-Co alloys by coupling the thermodynamic and kinetic calculations. The microstructure evolution was simulated and discussed in details. The numerical results are consistent with the experimental ones. They demonstrate that the cooling rate during the nucleation of the (Ni, Co)-rich dispersed-phase droplets (DPDs)/DPPs has a dominant influence on the solidification microstructure. The effect of Ostwald ripening of the DPDs/DPPs during solidification is very weak under the present cooling conditions. Graphic abstract