These are marked on the map with the sigil of Gondor.
To make it easier to find them, scan for them using the Haedir towers.
There are a five cities that have artefacts.
Minas Ithril (it has been pointed out on the forums that once Act One is completed, Ithril opens up again as Minas Morgul - Thanks to The AllSlayer for confirming)
There is one, in Seregost, that will require you to gain a skill to get in to the cave to pick it up (you can only see it by air).
Follow the quest line for Carnen and eventually you'll unlock 'Summon Dragon' from the Beast skilltree.
There is also another way, but it relies on hoping that a Drake spawns naturally using shadow mount.
Either way you'll also need to unlock shadow mount, as the Drake always spawns in the air.
Fly towards to ice wall (West to East) and you'll see a cave in the waterfall covered in ice, which makes it unclimbable.
Fly so the Drakes head is inside to cave and dismount, it might take a few attempts to get Talion to go in to cave instead of falling to the floor and having tk shadow mount again.
Below is a map of the offending artefact.
Note: You can climb the ice frozen waterfall to reach the artefact too. If you're struggling to find out where to climb you can still use a Drake. (Thanks to FreshBlood 21)