Information in this section was contributed by Niceguy62131121.
Bilbo's Map (Aragon, Frodo, Legolas)
Found in a Dimril Dale map. An elf will ask you to recover a lost item from some Orcs. Two Orcs will be guarding a chest and one of them will drop the artifact when you kill it.
Narsil, the Sword of Isildur (Aragorn, Legolas)
Found in Lothlorien at the bottom of the map. It can also be found by Frodo in Crinfanti.
Chain Link of Morgul (Aragorn, Legolas)
Found near the end of a Rohan map called the "East Wall". You start the level between three bushes (one big on the right and two smaller ones on the left). A bright blue Troll will appear and start running away. It invincible, but you can follow it to a cave. The chainmail will appear there.
Sauron's Ashes (Aragorn, Gandalf, Legolas, Frodo)
This is found in a tower at Helm's Deep up a large flight of stairs in the "Gorge" level to the north. It is the map immediately after you defend the broken wall with Gimli. A chest will appear to the left of the forge after opening all the boxes and chests on the northeast wall. Frodo does not go to Helm's Deep, but he can find the Ashes in a Mordor or Emyn Muil map.
Moria's Lamp (Legolas)
In the map where Legolas, Aragorn, and Gimli meet Gandalf, Moria's Lamp is hidden in a secret area at the top of the map. You have take a path to the right of the screen and group, then left. When you walk into the edge of the screen, you will disappear to another area where you can easily get the lamp.
Balin's Book (Gandalf)
This is found in Balin's Tomb before the Cave Troll enters, just below the actual tomb.
Troll Tusk (Frodo)
Found in Moria (just after the bridge of Kaza-dum). The Troll Tusk can be found in the northeast corner.
Judkins Scrolls (Eowyn)
In one map, a woman will ask you to clear town hall (a large building in the center of the area). Instead of immediately going in, go near it, then wander around the level for awhile, killing things and collecting items. When you return (usually), you can find the artifact in front of a wood pile to the west of the town hall door.