Three design methods for wireless power transmission (WPT) systems using antenna arrays have been investigated. The three methods, corresponding to three common application scenarios of WPT systems, are based on the method of maximum power transmission efficiency (MMPTE) between two antenna arrays. They are unconstrained MMPTE, weighted MMPTE, and constrained MMPTE. To demonstrate the optimal design process with the three methods, a WPT system operating at 2.45 GHz is designed, simulated, and fabricated, in which the transmitting (Tx) array, consisting of 36 microstrip patch elements, is configured as a square and the receiving (Rx) array, consisting of 5 patch elements, is configured as anL shape. The power transmission efficiency (PTE) is then maximized for the three application scenarios, which yields the maximum possible PTEs and the optimized distributions of excitations for both Tx and Rx arrays. The feeding networks are then built based on the optimized distributions of excitations. Simulations and experiments reveal that the unconstrained MMPTE, which corresponds to the application scenario where no radiation pattern shaping is involved, yields the highest PTE. The next highest PTE belongs to the weighted MMPTE, where the power levels at all the receiving elements are imposed to be equal. The constrained MMPTE has the lowest PTE, corresponding to the scenario in which the radiated power pattern is assumed to be flat along with the Rx array.