Excited-state energy migration among a collection of pigments forms the basis for natural light-harvesting processes and synthetic molecular photonic devices. The rational design of efficient energy-transfer devices requires the ability to analyze the expected performance characteristics of target molecular architectures comprised of various pigments. Toward that goal, we present a general tool for modeling the kinetics of energy migration in weakly coupled multipigment arrays. A matrix-formulated eigenvalue/eigenvector approach has been implemented, using empirical data from a small set of prototypical molecules, to predict the quantum efficiency (QE) of energy migration in a variety of arrays as a function of rate, competitive processes, and architecture. Trends in the results point to useful design strategies including the following : (1) The QE for energy transfer to a terminal acceptor upon random excitation within a linear array of isoenergetic pigments decreases rapidly as the length of the array is increased. (2) Increasing the rate of transfer and/or the lifetime of the competitive deactivation processes significantly improves QE. (3) Qualitatively similar results are obtained in simulations of linear molecular photonic wires in which excitation and trapping occur at opposite ends of the array. (4) Branched and cyclic array architectures exhibit higher QEs than linear architectures with equal numbers of pigments. (5) Dramatic improvements in QE are achieved when energy transfer is directed by a progressive downward cascade in excited-state energy. (6) The most effective light-harvesting architectures are those where isolated pools of donors each have independent paths directly to the terminal acceptor. Collectively, these results provide valuable insight into the types of molecular designs that are expected to exhibit high efficiency in overall energy transfer.