I configured my Jenkins server to only use HTTPS and enabled security. As well I don\'t like anybody who\'s not logged on to see the Dashboard (even if it would be empty). Here
For Jenkins servers without anonymous access, you can use Catlight build notification tool. You can provide access token or username/password to authenticate to your server.
I you have a self-signed ssl certificate, make sure that you add it to trusted by OS. That way, most applications will recognize it and connect to server without warnings.
Adding to @MrBlueSky 's answer, you can avoid the password expiration hassle; simply use a Jenkins-issued API Token instead of your password.
Configure
(in the left navbar)Show API Token
I've just started using the cctray Jenkins transport extension. Early days, but it seems to work as advertised and is connecting to our secure server perfectly happily.
Currently, the only significant limitation seems to be that if your password expires there's no way to re-enter your credentials.