Of the about 300 gas-phase molecular species so far detected in the interstellar medium (ISM), mostly via observations of their rotational lines, around 40% contain nitrogen (N) atoms. Likewise, of the less than a dozen interstellar molecules, firmly or likely detected in the solid-state water-dominated icy matrix by means of infrared observations, two bear N. A crucial parameter that regulates whether a species is in the gas or adsorbed on the icy phase is their binding energy (BE) toward the icy grain. Therefore, an accurate quantification of the BE is of paramount importance to properly model the ISM chemistry through numerical models. However, very few BEs are available in the literature, either determined experimentally or theoretically. In the present study, we calculate the BEs of 21 among the most abundant interstellar N-bearing species. We adopted two structural water ice models, representing a crystalline and an amorphous surface, using a reliable cost-effective procedure based on the density functional theory. While on the crystalline surface model only one BE per species is obtained due to the high symmetry of the unit cell, on the amorphous model from 5 to 10 BEs are obtained, due to its richer surface morphological variety. Most of our computed BEs agree with available experimental and other computational values. Finally, we discuss how the newly computed BEs can help estimate which N-bearing species can be frozen at the water snow line and, therefore, incorporated in water-rich ice planetesimals.