At the moment it seams that having a completed artifact gives no real benefit other than just being an item to show off in a museum or stash away to hopefully sell one day.
As in incentive to complete artifacts and a bonus for actually managing to do so (its not easy) I suggest that each one should offer a specific but not hugely game changing passive effect when in your inventory.
For example:
A completed wooden apple could give a +4 bonus to harvests when collecting from tree's.
A completed chicken shaped brick could give a +4 collection bonus to nibbling pigs, milking butterflies and squeezing chickens.
The platinum spork could give you a % of bonus energy when eating food.
The fake nose made of china could give you a bonus to cooking in some way.
The glove darned with a metal finger could give you an extra 2 chunks of metal or ore from mining.
The magical pendant could give you a bonus to meditation.
The torn manuscript could give you 2 energy free teleports per day.
The large mysterious cube could slightly increase your drop rate.
The mirror could give you 3 full mood boosts per day when used.
And the butterfly bone hair clip could give you a slight chance of getting a free item when walking past a vendor (one chance per vendor per game day)
These are just examples of what they could possibly grant.
If you like this idea or have any of your own to add or any comments please feel free to post!