This study narrates the implementation of remote assessment during the COVID-19 pandemic education in Ukrainian higher education institutions, based on exploring the reflections of 600 students and 150 educators. A wide range of student and faculty members experiences from Ukrainian higher education institutions were aggregated and analyzed. The data were collected through the Google Forms survey. The research focuses on the challenges of remote e-learning assessment during the COVID-19 crisis encountered by Ukrainian educators and learners and the approaches adopted to overcome them: learning designs, technological solutions, evaluation systems, and academic integrity measures. The current study also looks at the currently used platforms and applications that can assist in enhancing academic integrity and reinforcing education during pandemics and the various technological interventions to teaching, learning, and assessing that have been introduced or continued in higher education institutions around the world, and how they may have helped reduce the likelihood of students committing misconduct during the pandemic's emergency distance learning. The major outcome implies that addressing the issues of online assessment, cheating, and plagiarism on multiple levels is necessary, including boosting student knowledge and ethics; overcoming the resistance of the conservative part of the participants in the educational process to educational innovations due to the relatively low level of their mastery of modern educational technologies; training teachers to detect cheating methods; and applying severe sanctions on those who engage in such practices.