Search Alerts
You can set search alerts in many library databases so that you are automatically notified when a new source that meets your search criteria is added to the database. Below is a list of tutorials for various database vendors and Google Scholar.
Journal Alerts
Some journals allow you to sign up for alerts when a new issue is available. This information can usually be found on that journal's website and will vary depending on the journal's publisher.
Just as you should check to see what a source has cited for additional sources related to your topic, you can also identify where a source has been cited since it was published. These features are not 100% accurate, but they can still be useful.
Google Scholar
Google Scholar results can be a little messy, but it does a decent job of identifying citations in the humanities.
More information about cited reference searching can be found here: