I am on Joomla 3.9.16 currently with JEM 2.2.3. I guess the update mechanism for JEM has not been fully integrated with Joomla as when I go to Extensions->Update->Find Updates it does not tell me about a new version of JEM. Fine BUT when I go to Components->JEM->Update Check it tells me I'm on 2.2.3 and that this is the latest version of JEM. This is a bug I guess?
The update mechanism was implemented in JEM 2.2.3 and should work as expected. If not, then try to delete your cache and search for updates again. I have not heard from anyone that it did not do the job.
The Update Check in JEM itself was not yet updated to JEM 2.3.0. I just fixed that. This should work now..
Thanks for the reminder: The update check is obsolete and will be deleted in the next version.