Android apps
Home Network SSL Checker
This app checks in configurable intervals if a given HTTPS URL is reachable and the server identifies itself with the right certificate. It consists of a home screen widget displaying the status with colored "signal lights".
Checking... 
Okay... 
Unreachable... 
Wrong certificate... 
When checking and when an error happens, the global synchronization setting is turned off. This way you should be reasonably safe that the synchronization does not try to connect to a server whose identity is not verified, given it is the same server as the one you check.
More documentation...
Source package (388k, zip (Java))
...more to come...