We study the quantum properties of certain BPS Wilson loops in N = 4 supersymmetric Yang-Mills theory. They belong to a general family, introduced recently, in which the addition of particular scalar couplings endows generic loops on S³ with a fraction of supersymmetry. When restricted to S², their quantum average has been further conjectured to be exactly computed by the matrix model governing the zero-instanton sector of YM₂ on the sphere. We perform a complete two-loop analysis on a class of cusped Wilson loops lying on a two-dimensional sphere, finding perfect agreement with the conjecture. The perturbative computation reproduces the matrix-model expectation through a highly non-trivial interplay between ladder diagrams and self-energies/vertex contributions, suggesting the existence of a localization procedure.