Note that the below methods is implemented easiest if used together with Scott Helme's Report URI service. It however features email notifications only in paid plans. Otherwise, you have to log in and check the stats manually from time to time.
Using CAA and CT, it is possible to be notified by email when a CA issues a certificate for your domain name. Also see the DNS CAA and Web Reporting and Monitoring articles.
NEL, MTA-TLS, DMARC & CSP Reporting
As outlined in the Web Reporting and Monitoring and Mail Reporting and Monitoring articles, you can also monitor multiple different things related to your web and mail security.