Edible insects, such as mealworms (Tenebrio molitor larvae; TM) and crickets (Acheta domesticus; AD), are a sustainable, protein-dense novel food with a favorable amino acid profile, which might be an alternative to animal proteins. To assess the protein quality of TM and AD, we assessed the digestible indispensable amino acid scores (DIAAS), considering individual amino acids and their ileal amino acid digestibility, using an in vitro model based on the INFOGEST digestion protocol. In addition, we evaluated if various processing and food preparation steps influenced the in vitro digestibility of individual amino acids and the in vitro DIAAS values of TM and AD and compared them to chicken breast as a reference of excellent protein quality. The total protein in vitro digestibility ranged from 91 to 99% for TM and from 79 to 93% for AD and was negatively affected by oven-drying and, to a lesser extent, by chitin-reduction. The in vitro DIAAS values were 113, 89, and 92 for chicken, blanched TM, and blanched AD, respectively, when considering the indispensable amino acid (IAA) requirements of young children between 6 months and 3 years. Across different processing and food preparation methods, the in vitro DIAAS values ranged between 59 and 89 for TM and between 40 and 92 for AD, with the lowest values found in chitin-reduced insects. Due to their similarities to chicken regarding protein composition, total protein in vitro digestibility, and in vitro DIAAS values, TM and AD might be an alternative to traditional animal proteins, provided that suitable processing and food preparation methods are applied. Our in vitro DIAAS results suggest that TM and AD can thus be considered good-quality protein sources for children older than 6 months. The DIAAS calculations are currently based on crude protein (total nitrogen × 6.25), resulting in an overestimation of insect protein content, and leading to an underestimation and potential misclassification of protein quality. The in vitro model applied in this study is a valuable tool for product development to optimize the protein quality of edible insects. Further studies are required to assess the in vivo DIAAS of insects in humans.