Niobium (Nb) is a transition metal commonly used as an alloying element for increasing strength, toughness, corrosion resistance, and other properties of steel and superalloys. Pure Nb, however, is a very interesting metal for its excellent superconductivity. This makes it suitable for producing superconducting magnets and devices for particle acceleration systems and particle physics research (e.g., superconducting resonant cavities). In this work, the production of Nb by the Laser-Based Powder Bed Fusion (PBF-LB/M, also known as Laser Powder Bed Fusion or LPBF) process was examined. Manufacturing parameters were investigated to achieve additively manufactured parts with a relative density higher than 99.5% and showing a down-skin surface roughness in the range of 20–70 μm, depending on the inclination angle. Studies related to the limiting angle of self-supported Nb parts were also conducted, and innovative non-contact supporting structures were successfully developed. These allowed to creation of parts with very small overhang angles, without compromising the downward-facing surfaces; indeed at the same time, the as-built surface finish was improved.