Interaction energies of dimers containing alkaline earth (Be, Mg, and Ca) metals have been investigated using symmetry-adapted perturbation theory (SAPT) and supermolecular (SM) methods. Also, to enable broader comparisons, some calculations have been performed on the Zn dimer and on the He-Mg dimer. Although all of the investigated metallic atoms have closed electronic shells, the quasidegeneracy of the ground states of these atoms with the lowest-lying excited states leads to convergence problems in theories based on a single-determinant reference state. The main goal of the present work was to establish how the quality of the interaction energies computed using various electronic-structure methods changes across the range of atoms. We show that although the convergence problems become somewhat less severe with the increase of the atomic number, single-determinant-based methods do not provide reliable interaction energies for any of the investigated metallic dimers even at the level of the coupled-cluster method with single, double, and noniterative triple excitations [CCSD(T)]. However, interaction energies accurate to within a few percent can be obtained if CCSD(T) calculations in large basis sets are extrapolated to the complete basis set limit and followed by full configuration interaction (FCI) calculations with a frozen-core (FC) approximation. Since the systems considered contain only two valence electrons, FCI/FC calculations have been feasible for all of them except for Zn-2, providing the best theoretical estimates of the binding energies to date. We found that a large part of the error of the SAPT results originates from limiting some exchange components to terms proportional to the squares of the intermonomer orbital overlap integrals. When the neglected terms were approximately accounted for, the accuracy improved significantly and became comparable to that of CCSD(T), allowing us to obtain for the first time a physical interpretation of the interaction energies in metallic dimers.