A manifold of Λ + S and Ω electronic states of strontium monofluoride for energies below 40,000 cm−1 is characterized at the CASSCF/MRCI+Q level of theory. Potential energy curves and the associated spectroscopic parameters, as well as dipole moment and transition dipole moment functions, and transition probabilities given by the Einstein coefficients for spontaneous emission, and the associated radiative lifetimes are reported for the first time in the literature. A very accurate dissociation energy is determined for the ground state, and a set of spin-orbit constants derived for the 2Π and 2Δ states. All data needed to guide the experimental investigation of the yet unknown 2Δ state are provided, including estimates of transition probabilities and a radiative lifetime of about 1700 µs for v′= 0. This study places the D 2Σ+ state slightly below the C 2Π with a crossing near R = 4.0 a0, responsible for perturbations in the observed spectra, and locates a new 2Σ+ state near 32,000 cm−1, a region with a couple of close-lying states of difficult theoretical and spectroscopic investigation.