In Scotland anything found belongs to the Crown, not the Landowner. We use a system which although not perfect, does control where the artifacts end up.
if you find something of interest, you must by law, report it to the Treasure Trove Unit. The find is handed in, along with details of find spot and method of finding (eyes only, metal detecting, ploughing, etc). If T.T. Decide to keep it, they award an ex gratia payment to the finder.
The landowner has no rights in this at all, but most Detectorist have private agreement with land owners, to share any award for finds of interest made. Sometimes you can even be lucky enough to have your claimed item displayed in a museum.
if your artifact or coin is not claimed by Treasure Trove, then you get it back, with a certificate of provenance.
not a perfect system, but better than some.