In the search for coordination compounds showing significant second harmonic generation (SHG) activity, reaction of Ag(I) ions with the 4-hydroxypyrimidine (4-Hpymo) and 5-nitro-2-hydroxypyrimidine (HNP) ligands generated four crystalline 1D polymers, Ag(4-pymo)·nH2O (n = 2.5, 0), Ag(NP)(NH3), and Ag(NP), the latter two crystallizing in acentric space groups. Their synthesis, complete characterization, and structural determination, by conventional single-crystal and laboratory X-ray powder diffraction methods, are presented and discussed in the frame of diazaaromatic-ligand- and metal-containing species. XRPD has also allowed the detection of the polyhydrated, elusive Ag(4-pymo)·nH2O (n = 2, 3) species. Powders of Ag(NP) have shown an SHG activity close to that of standard urea. By applying the geometrical model proposed by Zyss, it is shown that the NP ligand is a highly promising chromophore, the oxo and nitro functionalities cooperatively promoting a high hyperpolarizability.