We wanted to setup a server for databasing and presenting high scores, but that dev needed to leave before it was stable, so  we're just encouraging players to post their high scores in the submission comments. Mentally, our  team has grouped the scores into two tiers, those with screenshots for proof, and those without, and it's so cool seeing people coming together.  Currently we're at 17 meters with a screenshot, and 9 meters without)
https://itch.io/jam/gmtk-2019/rate/463076
How are your games managing high scores?