We present a simple yet accurate numerical approach to compute the free energy of binding of multivalent objects on a receptor-coated surface. The method correctly accounts for the fact that one ligand can bind to at most one receptor. The numerical approach is based on a saddle-point approximation to the computation of a complex residue. We compare our theory with the powerful Valence-Limited Interaction Theory (VLIT) [P. Varilly et al., J. Chem. Phys. 137, 094108 (2012); S. Angioletti-Uberti et al., ibid. 138, 021102 (2013)] and find excellent agreement in the regime where that theory is expected to work. However, the present approach even works for low receptor/ligand densities, where VLIT breaks down.