Robust organic triradicals with high-spin quartet ground states provide promising applications in molecular magnets, spintronics, etc. In this context, a triradical based on Blatter’s radical has been synthesized recently, having two low-lying non-degenerate doublet states with a quartet ground state. The traditional broken-symmetry (BS)-DFT computed doublet–quartet energy gaps are reported to be somewhat overestimated in comparison to the experimentally observed values. In this work, we have employed different ab initio methods on this prototypical system to obtain more accurate doublet–quartet energy gaps for this triradical. The spin-constraint broken-symmetry (CBS)-DFT method has been used to reduce the overestimation of energy gaps from BS-DFT. To address the issues of spin-contamination and the multireference nature of low-spin states affecting the DFT methods, we have computed the energy gaps using appropriately state-averaged CASSCF and NEVPT2 computations. Using a series of active spaces, our calculations are shown to provide quite accurate values in concordance with the experimentally observed results. Furthermore, we have proposed and modeled another two triradicals based on Blatter’s radical, which are of interest for experimental synthesis and characterization. Our computations show that all these triradicals also have a quartet ground state with a similar energy difference between the excited doublet states.