If users are active on GitHub, you might be able to catch their email address from a commit log or open up an issue on a project they are working on.
If they are inactive however and don't have a visible email or repository there doesn't seem to be a direct way. I came up with this workaround that might be worth a try in extreme cases:
- create an empty repository
- add a README.md to it containing your message and include a reply email
- go to the
Settingsof that repository - send the repository via
Transfer Ownershipto the user in question
This should produce a notification for the user and allow him to contact you.
In cases when a user account is completely dead and you just want to get rid of it so that you can use the name for your own projects, you can also contact support, they will remove dead accounts: