Development of Pb-free superconducting solders is of great importance for the superconducting magnet manufacturers who often use Pb-Bi alloys as superconducting solders. Here, we study the phase evolution, microstructure, and superconducting properties of a number of alloys in the Pb-free Sn-In-Bi system using analytical scanning electron microscopy, differential thermal analysis, X-ray diffraction, and SQUID magnetometry. All the alloys exhibit melting points below 200 degrees C and superconducting transition temperatures above 4.2 K. The choice of initial composition and cooling rate controls the microstructure ( chemistry, volume fraction, morphology, and scale) of these alloys and strongly influences the final superconducting properties. The In-rich beta-phase shows better superconducting properties compared with the other phases in the Sn-In-Bi system. As a result, by increasing the indium content in the alloy, volume fraction of the In-rich beta-phase increases, leading to lower melting point, higher wettability, and better superconducting properties.