My organization is working on migrating to using Portal/Enterprise 10.8. Previously, all our web maps/apps were consumed in ArcGIS Online. Certain users had AGOL user types/roles that allowed them to edit data that references our REST endpoint feature service. Our current plan has been to migrate internal web apps/maps to Portal and have users edit "new" versions of these web maps referencing features services residing in the server we've federated with the Portal. As it turns out, due to license limitations, we can no longer furnish enough users with editing capabilities to continue the same workflows as we had previously.
"No answer was the stern reply" after a year, so I suppose sadly that there is no REST interface to webmaps, which is what I wanted to do to get a thumbnail using all the nice formatting in the webmap by someone else.
FWIW (very late reply)... The direct url format given above is correct, but it's for a mapservice, from a server; not for a webmap, from a portal. To retrieve portal data via a direct url, you'll first need to know its itemid (snoop around a bit). AND, it needs to be shared publicly (or you'll have to separately deal with the oauth stuff). Start by testing this base (this is mainly to verify you didn't change the default name/port/etc):
(adjust as needed for your specific install until successfully reach portal's rest root)
Then, for the portal item's metadata, append: /content/items/abcdef0123456789/itemdata?f=json
(where "abcdef0123456789" is the itemid of the portal item desired)
Or for the actual webmap data itself, instead append: /content/items/abcdef0123456789/data?f=json