The conventional practice of heat-resistant nickel-alloys’ brazing involves the utilization of industrial Ni-Cr-(B, Si)-based filler metals. However, employing filler metals within this system results in the formation of brittle compounds, specifically, silicides and borides of nickel, chromium, and other elements. These brittle phases have the potential to diminish the mechanical characteristics of brazed assemblies. This study investigates the feasibility of developing multicomponent high-entropy filler metals for brazing Ni-based alloys (specifically, heat-resistant ones) without including boron and silicon in their composition. Utilizing computational methods and the updated Hume-Rothery rules, we identified a promising NiCoCrAl-(Ti, Nb) system. Various thermodynamic parameters are computed, and corresponding dependences on the alloying-components’ content are established. The alloying limits of experimental alloys are determined, aligning with the criteria established for high-entropy alloys (HEA). Melting temperatures are calculated, and the liquidus-surface area of the NiCoCrAl-(Ti, Nb) system is delineated. Based on the research findings, it is determined that this alloy possesses a dendritic structure with some amount of eutectic component, and its melting temperature below 1220°C makes it suitable for brazing heat-resistant nickel alloys.