The diatomic dications SrF2+ and SrCl2+ were investigated for the first time at a high level of theoretical approach, SA-CASSCF/MRCI. The overall energetic profile of all Lambda + S states correlating with the three lowest dissociation channels, and the associated Omega states provide reliable results to characterize the lowest-lying states as thermodynamic stable. Einstein spontaneous emission coefficients evaluated for perpendicular A(1/2)-X-1(3/2) transitions, and parallel and perpendicular A(1/2)-X-2(1/2) ones, and the spectroscopic parameters are expected to guide the spectroscopist in the challenging task of probing them experimentally. Similarities and differences with the CaF2+ and CaCl2+ results are discussed.