At Morpht we monitor websites in a number of ways to ensure that we keep abreast of their health and are notified as soon as there is an issue.
Uptime monitoring: The highest level of monitoring which checks to see if the site is up and running. Monitoring can be simple and limited to a page returning a 200 response. A page can also be checked for returning a certain result to ensure that it is operational.
Error logging: The application or webserver will emit error messages from time to time. It is vital that these are logged into a system where they will be retained for later analysis. We use tools such as Kibana to review logs of this nature, or Logstash to detect errors in logs and alert or take a corrective action automatically.
Search Console: Google offers a search console which will report on content problems on the site. This is helpful for identifying broken links and content issues.
Site quality tools: There are a number of providers of SaaS tools which are able to monitor the site for quality. Such tools include Monsido and SiteImprove. Both of these tools can be helpful for large organisations where monitoring of quality of content across a number of pages is vital.