Fusion splicing is an already mature technology used to join the ends of optical fibers in the telecommunication industry. However, there is a lack of reliable and well-described protocols to join the ends of fused silica microtubes or capillaries using fusion splicing. In this work, a step-by-step procedure is proposed and demonstrated to find the optimal operation conditions to splice the ends of fused silica capillaries by fusion. The two most appropriate and known technologies were tested and optimized: the microfurnace technique (or hot filament technique) and the electric arc technique. It is shown that both produce good splices when the capillaries are well cleaved. For this reason, the removal of the external coating, which is important for good cleavage, was also revised. The cleaving techniques were also compared among themselves. As a result, fusion splices of cylindric-to-cylindric, cylindric-to-square, and square-to-square capillaries are demonstrated. They have potential applications in new detection schemes and separation layouts in capillary electrophoresis, electrophoresis-based hydrodynamic concentrators, chromatography, cell sorters, and microfluidics in general.