Capistrano and Jenkins can be used together to automate the build, deployment, and management of Java web applications on clusters of servers. Capistrano allows deploying code to multiple servers and managing services, while Jenkins provides continuous integration by automatically building, testing, and deploying code changes to different environments like development, testing, and production. When a build succeeds in Jenkins, it can trigger Capistrano tasks to deploy the new code to servers and restart services. This achieves automated and versioned software releases across server clusters.