Curved carbon pi surfaces have chemical and physical properties suitable for exploitation for chemical microencapsulation and the self-assembly of nanoscale materials. Advances will greatly benefit from more understanding of their host-guest interactions with guests such as metal cations. Here, quantitative predictions are made for the binding of metal cations to three prototypical surfaces using density functional theory calculations: the buckybowls C(20)H(10), C(30)H(10), and C(40)H(10). The focus was on finding the most favorable binding sites, assessing whether binding is more favorable inside or outside the bowl, and exploring factors influencing the binding site preference. Classes of cations studied included small and large monocations and cations with multiple charges: Na(+), Cs(+), NH(4)(+), Ba(+), Ba(2+), and La(3+). Factors found to favor inside binding were large ion size and high ion charge, suggesting that polarization interactions as well as short-range interactions are important in determining the preferred binding sites inside and outside these buckybowls. Unlike monocations, which at best have only a weak tendency toward encapsulation, the multiply charged cations Ba(2+) and La(3+) were found to have a strong driving force toward containment inside the bowls. Coulomb potentials were found to favor cation binding on the outside surface of the bowls, but cation microsolvation through polarization interactions presents a compensating factor that can tip the balance in favor of encapsulation. Knowledge of these factors will be a valuable tool in the design of nanocontainers and the diverse architecture possible with these structural elements.