Abaqus provides some error estimates (here called error indicators) as output variables for implicit analyses. However energy norm error is not available. You would have to operate on field output data in Viewer or use scripting to get additional output like that.
If you are thinking of the energy norm as an implicit solution control, then Abaqus/Standard does not offer it. It's a weak criterion that is easily fulfilled so some codes do not bother putting it out there. I haven't used Abaqus in a few years so things may have changed.
*********************************************************
Are you new to this forum? If so, please read these FAQs: