Extensive recent development and deployment of electric-powered unmanned aerial vehicles (UAVs) has placed increased focus on the design of quiet propellers for these vehicles. To aid in this effort, a design methodology is developed to synthesize low-noise and efficient propellers for electric UAVs. This methodology employs a blade-element momentum theory performance analysis method, a compact-chord aeroacoustic analysis method based on Farassat's Formulation 1A of the Ffowcs Williams-Hawkings equation, and a beam analogy aeroelastic model. Blade geometries that minimize induced and profile losses are analytically determined, and other design parameters are chosen parametrically to balance noise reduction and aerodynamic performance. Various noise-reduction techniques and their impacts on propeller performance are analyzed, and reduced tip speeds and increased blade counts are selected as most promising for the chosen conditions. Two propellers of different blade counts designed using this methodology are manufactured to validate the methodology, and static test stands are developed to perform this validation. Comparisons between the predicted and experimental performance reveal a deficit in thrust; this is partially explained by the inaccurate wake geometry assumptions of the blade-element momentum theory at static conditions. The remainder of this discrepancy is likely attributable to a combination of experimental error and rotational and three-dimensional aerodynamic effects not analytically modeled. A significant noise reduction was experimentally demonstrated between propellers of low and high blade counts, validating trends identified analytically; this reduction, while large, was less than the predicted magnitude, likely due to manufacturing irregularities limiting destructive acoustic cancellation between propeller blades. Although the performance discrepancy precludes the use of this methodology for the design of production propellers, the methodology is valuable in easily identifying practical quiet propeller configurations for preliminary design studies.