What do I do with a ground wire on an new ceiling fixture when there is none coming from the ceiling? I have a very old home with plaster ceilings.

Not much you can do without running a new ground wire. But, check for a box ground by testing from black to box with a VOM. Some older homes wired with BX would have the armored case as a ground. If it shows voltage connect the ground to the box. If none, tape the ground end and put it back in the ceiling box.

Time Out, please.

Running a new ground wire is not allowable.

The entire circuit has to be redone (from the main panelboard to the outlet) with cable that is listed for the needed amperage.