Recently there has been significant interest in manipulating the self-assembly behavior of block copolymers to obtain structures that are not observed in the bulk. Here we explore the conditions for which self-assembly in laterally confined thin block copolymer Films results in tetragonal square arrays of standing up cylinders. More specifically, we used self-consistent-field theory (SCFT) to study the equilibrium phase behavior of thin films composed of a blend of AB block copolymer and A homopolymer laterally confined in square wells. By using suitable homopolymer additives and appropriately sized wells, we observed square lattices of upright B cylinders that are not stable in pure AB block copolymer systems. We further investigated the optimal conditions and parameters that lead to defect-free, in-plane tetragonal ordering. Considering the potential application of such films in block copolymer lithography, we also conducted numerical SCFT simulations of the role of line edge roughness at the periphery of the square well on feature defect populations. Our results indicate that the tetragonal ordering observed under square confinement is robust to a wide range of boundary perturbations.