The first quantitative evidence for the viability of three-dimensional aromatic clusters involving d-orbitals in pseudo-octahedral coinage metal cages M6Li2 (M = Cu, Ag, Au) as well as in tetrahedral coinage metal cages M'Li-4(4) (M' = Cu, Ag) was obtained computationally. These cages exhibit many features similar to those of their square planar M4Li2 analogues. The large negative nucleus-independent chemical shifts (NICS) at the cage centers indicate three-dimensional delocalization. This diatropic character arises mostly from d-orbital delocalization combined with substantial contributions from the lowest-valence orbitals. The bonding molecular orbitals of the pseudo-octahedral clusters M6Li2 (M = Cu, Ag, Au) are analogous to those in similar octahedral clusters involving p-orbital delocalization (e.g., B6H62-). The M'Li-4(4) clusters exhibit two isomeric forms: metal tetrahedral cages tetracapped by lithium cations on the outside [(M'(4))(.)4Li] and lithium tetrahedra on the inside capped by coinage metal atoms on each of the four faces [(Li-4)(.)4M]. Whereas the (M'(4))(.)4Li type structure is preferred for copper, gold and silver favor the (Li-4)(.)4M arrangement. NBO-NICS analysis shows that the large diatropic character in (M'(4))(.)4Li structures is due to the favorable contribution from both s- and d-orbitals, whereas the small NICS values in the center of (Li-4)(.)4M are due only to the diatropic contributions from the s-orbitals.