We present a methodology for computing the binding energy of molecular dimers based on extrapolation of pseudospectral local second-order Moller-Plesset (MP2), or PS-LMP2, energies to the basis set limit. The extrapolation protocol is based on carrying out PS-LMP2 calculations with the Dunning cc-pVTZ (-f) and cc-pVQZ (-g) basis sets and then using a simple two-parameter function to compute the final basis set limit results. The function is parametrized to ultralarge basis set MP2 calculations for 5 molecular pairs taken from the literature and then tested by calculating results for a set of formamide dimers for which such calculations have also been carried out. The results agree to within ca. 0.2 kcal/mol with the conventional MP2 large basis set calculations. A specialized, but relatively simple, protocol is described for eliminating noise due to overcompleteness of the basis set. Timing results are presented for the LMP2 calculations, and comparisons are made with the LMP2 methodology of the QChem program. CPU time required by each of the methods scales as N(3), where N is the number of the basis functions, with the PS-LMP2 approach displaying a 2- to 3-fold advantage in the prefactor. We also discuss one set of test cases for which the PS-LMP2 results disagree with those obtained from an alternative type of MP2 calculation, N-methyl acetamide (NMA) dimers, and show that the results for liquid-state simulations using polarizable parameters derived by fitting to the PS-LMP2 binding energies appear to produce better results when compared with experimental data. The convergence issues associated with the alternative MP2 formulation remain to be investigated.