A series of boron-modified polysilazanes (BmPSs) of the type [B(C2H4SiCH3NCH3)3]n was synthesized by reaction of tris(dichloromethylsilylethyl)borane (B(C2H4SiCH3Cl2)3, TDSB) with methylamine (MA) using various MA : TDSB ratios and then characterized for suitability as precursors of Si/B/C/N ceramic fibers. Molecular chemistry and polymer structure of BmPSs are investigated in the present paper by elemental analyses, solid-state NMR and molecular weight measurements. It is shown that the MA : TDSB ratio fixed during the polymer synthesis strongly modifies the proportion of identified structural units, determines the boron environment and influences the molecular weight of polymers, causing different responses to melt-spinnability. Based on fiber shape visualization using a CCD camera during extrusion and stretching, appropriate melt-spinnable compounds are prepared with MA : TDSB ratios between 9.0 and 9.2. These polymers represent structurally complex networks composed of four- and/or six-membered –(Si–N)n– rings bridged via tri-coordinated BC3−xNx and tetra-coordinated BC4−xNx units. In such polymers, the proportion of terminal N(H)CH3 groups as well as the BC3−xNx : BC4−xNx ratio are especially tailored for melt-spinning. Such compounds display a chemical formula of [Si3.0B1.1C11.35±0.5N3.8±0.4H8.15±1.35]n with n ≈ 2.5. They have a glass transition temperature of 48 ± 4 °C, tailored flexibility and sufficient plasticity to successfully produce fine-diameter green fibers at 107 ± 8 °C in a stable melt-spinning process. After melt-spinning, green fibers have been cured then pyrolyzed up to 1000 °C to generate silicoboron carbonitride (Si3.0B1.0C5.0N2.4) fibers with 10–13 μm in diameter according to an established procedure. Polymer fibers have a ceramic yield of 44% after thermal decomposition at 1000 °C. The circular fibers exhibit a dense texture with a glassy section, indicating an amorphous state of the ceramic which was further confirmed by TEM as well as Weibull strengths of 1.4 GPa and Young's modulus of 120 GPa.