The understanding of interstellar nitrogen chemistry has improved significantly with recent results from the Herschel Space Observatory. To set even better constraints, we report here on deep searches for the NH+ ground state rotational transition J=1.5-0.5 of the ^2Pi_1/2 lower spin ladder, with fine-structure transitions at 1013 and 1019 GHz, and the para-NH2- 1_1,1-0_0,0 rotational transition at 934 GHz towards Sgr B2(M) and G10.6-0.4 using Herschel-HIFI. No clear detections of NH+ are made and the derived upper limits are <2*10^-12 and <7*10^-13 in Sgr B2(M) and G10.6-0.4, respectively. The searches are complicated by the fact that the 1013 GHz transition lies only -2.5 km/s from a CH2NH line, seen in absorption in Sgr B2(M), and that the hyperfine structure components in the 1019 GHz transition are spread over 134 km/s. Searches for the so far undetected NH2- anion turned out to be unfruitful towards G10.6-0.4, while the para-NH2- 1_1,1-0_0,0 transition was tentatively detected towards Sgr B2(M) at a velocity of 19 km/s. Assuming that the absorption occurs at the nominal source velocity of +64 km/s, the rest frequency would be 933.996 GHz, offset by 141 MHz from our estimated value. Using this feature as an upper limit, we found N(p-NH2-)<4*10^11 cm^-2. The upper limits for both species in the diffuse line-of-sight gas are less than 0.1 to 2 % of the values found for NH, NH2, and NH3 towards both sources. Chemical modelling predicts an NH+ abundance a few times lower than our present upper limits in diffuse gas and under typical Sgr B2(M) envelope conditions. The NH2- abundance is predicted to be several orders of magnitudes lower than our observed limits, hence not supporting our tentative detection. Thus, while NH2- may be very difficult to detect in interstellar space, it could, be possible to detect NH+ in regions where the ionisation rates of H2 and N are greatly enhanced.
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