A detailed study of the excited state energy migration dynamics that take place within an assembly of Ru(II) and Os(II) polypyridyl complexes linked together through a polymer backbone is presented. The energy migration process is initiated by the photoexcitation of the metal-to-ligand charge transfer (MLCT) transition in one of the Ru(III) complexes and terminated by energy transfer to a lower energy Os(II) trap. Energy transfer sensitization of Os(II) can occur in a single step if the excited state is formed adjacent to a trap, or after a series of hops between isoenergetic rutheniums prior to reaching a trap. The dynamics of the energy transfer process are followed by monitoring the growth of Os(II)* luminescence at 780 nm. The kinetics of the growth are complex and can be fit by a sum of two exponentials. This kinetic complexity arises both from the presence of a distribution of donor-acceptor distances and the variety of time scales by which Os(II)* can be formed. We have augmented the time-resolved experiments with Monte Carlo simulations, which provide insight into the polymer array's structure and at the same time form the basis of a molecular-level description of the energy migration dynamics. The simulations indicate that the most probable Ru*-->Os energy transfer time is similar to 400 ps while the time scale for Ru*-->Ru hopping is approximately 1-4 ns. The time scale for Ru*-->Ru hopping relative to its natural lifetime (1000 ns) suggests that this polymer system could be extended to considerably longer dimensions without an appreciable loss in its overall efficiency.