Are we talking Macs here? If so, go into Details on the Mac, in the Computer Information tab, click on the (-) icon in the upper right. then uncheck the "Manage this computer" checkbox. Click Save. That Mac is now unmanaged from the perspective of the JSS.
Couple of things to note, the launchagent on the client Mac will still do its regular "check-in" with your JSS, so the Last Contact Date will continue to update, but you will no longer be able to push any software to this machine. It won't be available in Scope tabs or in Casper Remote. It also won't submit any inventory, since that is controlled by a policy and policies won't run on an unmanaged Mac.
Also, if you decide to manage it again later, you need to re-enter the local account name/password for management. Once you click Save, the db gets updated and removes that info.

Ah. I don't need to know how to manage/unmanage machines myself; I need to give other JSS Users the ability to manage/unmanage machines. I'm trying to find out what permission in Casper allows this.

Oh, sorry, I misunderstood. I think the following 3 settings control that:

View Inventory Tab
View Details on Inventory Items
Edit Inventory Items

Thanks, that was exactly what I needed.