The molecular structures, the nuclear magnetic shieldings, and the aromatic ring-current shieldings (ARCS) have been calculated for Al-4(2-), Al4Li-, and Al4Cu- at the Hartree-Fock (HF) level, the second-order Moller-Plesset (MP2) level, the coupled-cluster singles and doubles (CCSD) level, and the coupled-cluster singles and doubles level augmented by a perturbative correction for triple excitations (CCSD(T)). The ARCS calculations show that the square-shaped Al-4(2-) ring sustains a very large diatropic ring current in an external magnetic field. Because the induced ring current is one measure of the molecular aromaticity, the Al-4(2-) ring can be considered aromatic. Molecular structure optimizations on the group IIIA analogues show that B-4(2-), Ga-4(2-), In-4(2-), and Tl-4(2-) also exist and have D-4h symmetry. The ARCS calculations indicate that they are aromatic, too. New neutral Al-4(2-) analogues such as Si2B2, Si2Al2, and Si2Ga2 are proposed. The molecular structure and ARCS calculations on the neutral analogues yield planar ring structures with large diatropic ring-current susceptibilities.