Globalization of all spheres of activity of educational systems determines the need to create simple and accessible tools for monitoring and evaluating the quality of objects and resources. In particular, due to the need to intensify the processes of digital transformation of education, it is important to assess the quality of digital educational environments (DEE). The aim of the work is to substantiate the approach and describe the procedure for monitoring of DEE of educational institutions based on the available cloud services, providing convenient collection, accumulation, and processing of statistical and monitoring indicators.The projective criterial model of the system of assessment and monitoring of the quality of DEE, which is based on the results of self-assessment of the educational organization and external expert evaluation, was adopted. The main feature of the model is the participation of organizations and external experts in the process of designing criterion rubrics, conducting and analyzing the results of monitoring. Yandex Forms service is used for self-assessment of DEE and expert evaluation of the educational organization website which allows converting of the collected data into spreadsheets. By combining the data and their statistical processing it is possible to obtain indicators for different slices and ratings, to conduct a summary clustering of the DEE of the studied organizations by three levels: low, average, and high.The proposed model was implemented in the assessment of DEE practices of supplementary education for children. To determine the quantitative and qualitative indicators of the DLE and the official sites of additional education organizations we created questionnaires in Yandex Forms filled in by the representatives of the studied organizations. Pilot testing showed that the collection, processing, and delivery of monitoring data to users was technologically simple and easy.The projective criterial model for assessing the quality of the DEE of supplementary education organizations can be used for many other studies related to criterion-based assessment activities.