In recent years, the Zn-Ag alloy demonstrated to be a potential candidate for biomedical applications as a bioabsorbable implant. Frequently, the microstructure of this alloy is composed of ε-AgZn3 dendrites enveloped by a peritectic η-Zn matrix, strongly influenced by the casting conditions. To study its growth, solidification experiments of the Zn-10.0Ag-1.0Mg wt% alloy were carried out on different copper mold geometries, including rectangular, wedge-shaped, and cylindrical. A range of microstructures between the limits of constitutional velocity (2.6 × 10−4 mm/s) and absolute stability velocity (3.3 × 102 mm/s) were achieved. Besides the ε-AgZn3 and η-Zn phases with different morphologies, Peritectic Coupled Growth (PCG) was found. The addition of Mg together with convection during solidification promotes PCG at a growth rate of ∼ 0.1 mm/s.