The current document is directed to methods and systems that generate microsegmentation quotients for computational entities and components of a distributed-computer-system. In the described implementation, microsegmentation quotients are generated for each component, subsystem, or computational entity, collectively referred to as “system entities,” of a set of specified system-entity types within the distributed computer system. Microsegmentation quotients are generated for system entities at any of the various hierarchical levels within a distributed computer system, including for the entire distributed computer system. Microsegmentation quotients are generated by an iterative process that refines initial estimates of the microsegmentation quotients for system entities within the distributed computer system. Microsegmentation quotients are displayed, through system-management interfaces, to administration and management personnel and provided to automated administration-and-management-system tools and facilities in order to facilitate analysis and monitoring of distributed-computer-system security as well as to facilitate rapid and accurate detection and amelioration of security-related deficiencies and problems.