External testing (i.e. testing from outside the CL-CEC web-application) is possible once your CL-CEC is installed, configured and registered. You can then drive the CL-CEC and its applications from the normal science UIs.
AstroGrid recommends the AstroGrid "workbench" for testing. Please see the separate documentation for that component. The workbench allows you to address the CL-CEC directly, independently of scripts and workflows. You can also run tests by submitting workflows from the an AstroGrid web-portal.
The exact test-cases depend on the applications for which your CL-CEC is configured, so no details can be given here. Good luck!