People with Autism Spectrum Disorder (ASD) have an affinity for technology, which is why multiple studies have implemented different technological proposals focused on the development of skills in people with ASD. Studies have evaluated the user experience (UX) and/or usability of their technological proposals through different evaluation methods, so they can be friendly and usable for users with ASD. However, the evaluation methods and instruments used do not consider the specific characteristics and needs of people with ASD, and furthermore, details are lacking in their implementations. To formalize the UX evaluation process, we propose a three-stage methodology to evaluate the UX in systems, products and services used by adults with ASD. The methodology considers in its processes, evaluation methods and instruments the characteristics of people with ASD so that, through the UX evaluation, the satisfaction and perception of these users about the system, product or service evaluated is improved. This proposal has been validated through the opinions of experts with knowledge in UX/Usability and ASD in two instances, which have contributed to specify, restructure, and improve the methodology.