Here is how I moved my jobs to cold storage using the Shelve Project plug-in

WARNING the Shelve Projects plug-in does not maintain data for the Job Config History plug-in. If you unshelve your project, the configuration history will be empty.

WARNING the Shelve Projects plug-in does not copy your builds if you have modified the config.xml to change buildsDir. (Note: I have not tried this on a clean unmodified installation - so I cannot guarantee it ever saves builds).

1. Right-click a project in the Jenkins GUI and press "shelve project"
2. Navigate to your Jenkins "home" folder (you can find this path from the GUI under Manage Jenkins > System Information > user.home)
3. Navigate into the the shelvedProjects subdirectory
4. Move both the .tar file and a .properties file for each project you would like to offload.
5. In Jenkins, view the "Shelved projects" and you will no longer see the projects you moved out.

Then later you can copy those files back, and the "Shelved projects" will now show the project you retrieved from cold storage.

Unfortunately, this process loses the Job Config History.