Boron-boron multiple bonds, such as those found in diborenes and diborynes, are typically stabilized by σ-donor ligands that furnish electron density to these otherwise electron-deficient species. These compounds are not only of fundamental importance in the study of chemical bonding, but can also activate small molecules in a chemistry reminiscent of that carried out by transition metals. In the pursuit of designing new and improved σ-donor ligands to stabilize diborenes and diborynes suitable to activate small molecules, we performed density functional calculations to evaluate the Lewis basicity of a series of σ-donor ligands. For this evaluation, we analysed the interaction between the boranes and the σ-donor ligands in model systems L!BX 3 (X=F and Me) using energy decomposition analyses. We found that electronic bond energies of the L!BX 3 adducts correlate well with the ionization energies of the ligands and that ligands with high or medium basicity stabilize diborynes better than ligands with low basicity. We also learnt that beryllium-based ligands are promising since they are able to stabilize L!B�B ! L diborynes without significantly reducing the triple bond character of the B�B bond.