In the In The Void level, get right to the very end and slowly walk over to the edge of the platform (the platform whereby if you jump off the edge the stage ends) and when the screen shakes, go to where you turned on the Blue Key Switch. The pillar that had the Doom Artefact will now have a switch on it. Use the switch and run all the way back to the Red Key door (quickly) and run towards the wooden bridge.

The artefact will be at the end of the bridge. Grab the artefact and then up the top should read: 'It must do something'. Now you can exit the stage.

If the artefact disappears before you can snare it, just repeat the entire method, right from the start.