The current document is directed to methods and systems that provide an automated augmented-reality facility for determining whether or not personal items and luggage meet airline requirements. In one implementation, a semi-transparent three-dimensional image generated from a model of a personal item or luggage item of the maximum dimensions allowed by an airline is displayed to a user, on a user device that includes a camera, within an electronic image of the real scene encompassed by the field of view of the camera. The user can then position a real personal item or luggage item at a point in space corresponding to the apparent position of the virtual image of the model and compare the dimensions of the real personal item or luggage item to the dimensions of the semi-transparent model volume in order to determine whether or not the real personal item or luggage item meets airline size requirements.