The residual coating stress and its control is of key importance for the performance and reliability of silicon nitride (SiNx) coatings for biomedical applications. This study explores the most important deposition process parameters to tailor the residual coating stress and hence improve the adhesion of SiNx coatings deposited by reactive high power impulse magnetron sputtering (rHiPIMS). Reactive sputter deposition and plasma characterization were conducted in an industrial deposition chamber equipped with pure Si targets in N2/Ar ambient. Reactive HiPIMS processes using N2-to-Ar flow ratios of 0 and 0.28–0.3 were studied with time averaged positive ion mass spectrometry. The coatings were deposited to thicknesses of 2 μm on Si(001) and to 5 μm on polished CoCrMo disks. The residual stress of the X-ray amorphous coatings was determined from the curvature of the Si substrates as obtained by X-ray diffraction. The coatings were further characterized by X-ray photoelectron spectroscopy, scanning electron microscopy, and nanoindentation in order to study their elemental composition, morphology, and hardness, respectively. The adhesion of the 5 μm thick coatings deposited on CoCrMo disks was assessed using the Rockwell C test. The deposition of SiNx coatings by rHiPIMS using N2-to-Ar flow ratios of 0.28 yield dense and hard SiNx coatings with Si/N ratios <1. The compressive residual stress of up to 2.1 GPa can be reduced to 0.2 GPa using a comparatively high deposition pressure of 600 mPa, substrate temperatures below 200 °C, low pulse energies of <2.5 Ws, and moderate negative bias voltages of up to 100 V. These process parameters resulted in excellent coating adhesion (ISO 0, HF1) and a low surface roughness of 14 nm for coatings deposited on CoCrMo.