I have a server running Windows Server 2012 R2 with IIS 8.5. I've configured it for remote management, and I am able to successfully connect to the IIS mangement service (on this server) from another computer, as long as I login with an "admin" account (an acct that's in the local Administrators group on the server).
I've tried to enable IIS Manager to allow non-admin accounts:
How can I get IIS to allow non-admins to connect to the remote management service?
UPDATE: Based on the answer given below, non-server-admins need to choose the IIS Manager option "Connect to a Site", not "Connect to a Server". When you choose that option, you'll need to specify the Server name and the Site name: