More and more universities are moving toward electronic exams (in short e-exams). This migration exposes exams to additional threats, which may come from the use of the information and communication technology. In this paper, we identify and define several security properties for e-exam systems. Then, we show how to use these properties in two complementary approaches: model-checking and monitoring. We illustrate the validity of our definitions by analyzing a real e-exam used at the pharmacy faculty of University Grenoble Alpes (UGA) to assess students. On the one hand, we instantiate our properties as queries for ProVerif, an automatic verifier of cryptographic protocols, and we use it to check our modeling of UGA exam specifications. ProVerif found some attacks. On the other hand, we express our properties as Quantified Event Automata (QEAs), and we synthesize them into monitors using MarQ, a Java tool designed to implement QEAs. Then, we use these monitors to verify real exam executions conducted by UGA. Our monitors found fraudulent students and discrepancies between the specifications of UGA exam and its implementation.