Two series of co-polymers with the general formula [B(C2H4SiCH3(NH)x(NCH3)y)3]n, i.e., composed of C2H4SiCH3(NH)x and C2H4SiCH3(NCH3)y (C2H4 = CHCH3, CH2CH2) building blocks in a well defined x : y ratio, have been synthesized by hydroboration of dichloromethylvinylsilane with borane dimethyl sulfide followed by successive reactions with lithium amide and methylamine according to controlled ratios. The role of the chemistry behind their syntheses has been studied in detail by solid-state NMR, FT-IR and elemental analyses. Then, the intimate relationship between the chemistry and the melt-spinnability of these polymers was discussed. By keeping x = 0.50 and increasing y above 0.50, i.e., obtaining methylamine excess, the co-polymers contained more ending groups and especially more tetracoordinated boron, thus allowing tuning very precisely the chemical structure of the preceramic polymer in order to meet the requirements for melt-spinning. The curing treatment under ammonia at 200 °C efficiently rendered the green fibers infusible before their subsequent pyrolysis under nitrogen at 1000 °C to generate Si-B-C-N ceramic fibers. Interestingly, it could be possible to produce also low diameter hollow fibers with relatively high mechanical properties for a further exploration as membrane materials.