In this study, we report on a Systematic Mapping Study (SMS) on how the quality of the quantitative instruments used to measure digital competencies in higher education is assured. 73 primary studies were selected from the published literature in the last 10 years in order to 1) characterize the literature, 2) evaluate the reporting practice of quality assessments, and 3) analyze which variables explain such reporting practices. The results indicate that most of the studies focused on medium to large samples of European university students, who attended social science programs. Ad hoc, self-reported questionnaires measuring various digital competence areas were the most commonly used method for data collection. The studies were mostly published in low tier journals. 36% of the studies did not report any quality assessment, while less than 50% covered both groups of reliability and validity assessments at the same time. In general, the studies had a moderate to high depth of evidence on the assessments performed. We found that studies in which several areas of digital competence were measured were more likely to report quality assessments. In addition, we estimate that the probability of finding studies with acceptable or good reporting practices increases over time.