Hartree-Fock (HF) and density functional theory (DFT) methods are known for having problems in predicting singlet-triplet energy splittings when the system displays significant diradical character. Multireference methods are traditionally advocated to deal with the spin-contamination problem inherent in broken-symmetry mean-field methods. In the present work, spin-contamination is rigorously eliminated by means of a symmetry projection approach, carried out in a variation-after-projection fashion, recently implemented in our research group. We here explore the performance of a variety of projected Hartree-Fock (PHF) approaches (SUHF, KSUHF, SGHF, and KSGHF) in predicting singlet-triplet energy gaps in a broad set of diradical systems: small diatomic molecules, carbenes and silenes, and a few larger molecules (trimethylenemethane and benzyne isomers). For most of these systems, accurate experimental data is available in the literature. Additionally, we assess the quality of the geometrical parameters obtained in SUHF-based optimizations for some of the systems considered. Our results indicate that PHF methods yield high-quality multireference wave functions, providing a good description of the ground state potential surface as well as an accurate singlet-triplet splitting gap, all within a modest mean-field computational cost.