All authentification requests while using Shibboleth are handled by the domain sso.rwth-aachen.de. The URL-bar of the browser should look as follows:
You can find details on the certificate by clicking on the lock in the URL-bar.
Click the lock
Afterward click on certificate(valid). This opens another window.
This view shows that the server-certificate is correct for sso.rwth-aachen.de, and that the certificate is issued by DFN-Verein Global Issuing CA. You can also find the valid from and valid until dates. To check the fingerprint of the certificate, click on "Details".
In this view, scroll down to the entry for "fingerprint", where you are shown the certificate's fingerprint.
Click the lock.
This view shows you if the connection is secure. A click on the arrow reveals the security details.
The important part is that the page sais "Verified by the DFN Foundation" To check the fingerprint, click on "further information" and navigate to the tab "security".
The entry "website-identity" shows the URL again, as well as who validated it. Clicking "show certificate" takes you to the certificate details and the fingerprint.
You can now check fingerprints, as well as other details of the certificate.