Awakened Unique Blades: What a Relic Becomes and What Each One Does
A 
Dormant Relic is not an ingredient. Simply Swords treats it as one of fifty-eight unique weapons, and the relics sit in a small group of their own alongside the 
Decaying Relic and the 
Enigma, apart from the forty uniques that simply turn up as loot.
There is no awakening recipe
This is the first thing to settle, because it saves a long and fruitless search. The mod ships ninety-two smithing recipes and not one of them takes a unique weapon as its base, produces a unique weapon, or involves a relic at all. Seventy-seven are compatibility tiers for another mod's metals and the remaining fifteen re-roll a runic weapon. No crafting grid, smithing table layout or furnace step converts a relic into a named blade, so any walkthrough that hands you a three-slot arrangement to copy is describing something the mod does not contain.
What the mod does point at is the 
Runic Forge. Its in-game description is a single line and it is exact: the block is used to awaken unique weapons. The 
Runic Tablet carries its own line about repairing and upgrading uniques, and it appears as the template in every re-roll recipe, paired with a diamond.
The relics themselves are the other half of the answer. Their in-game tooltips talk about carrying them rather than swinging them. The Dormant Relic reads that a faint power seems to emanate from within, and a later state of the same item describes that power as growing rather than faint. The Decaying Relic is the most direct of the three, telling its holder to keep it in their inventory while exploring the deepest and darkest depths of the Overworld.
What the awakened blades actually do
Each unique carries its effect in its own tooltip, and the real behaviour is more specific than a damage number suggests.
Frostfall is thrown rather than swung. Airtime and angle change its impact damage, and after it lands it pulses five times, damaging, slowing and pulling enemies toward it.
Bloodwake works through stacking Bleed. Striking an enemy that has reached maximum Bleed consumes the stacks in a blood burst, damaging everything nearby, spreading Bleed around the target and granting Blood Frenzy.
Brimstone Claymore summons a second claymore in the air above your target. It pulses area damage where it hangs, then plunges into the ground.
Arcanethyst has a chance on hit to levitate what it strikes, lifting nearby medium-sized enemies with arcane force before slamming them back down.
Hiveheart releases a single angry bee on hit, which stings the target and disappears. The effect runs on a cooldown, so it rewards steady contact rather than burst damage.
Choosing what to carry
Read the effects rather than the damage line. A thrown weapon that pulls a group together and a weapon that pays out only after Bleed has stacked ask for completely different fights, and neither is served by the habit of picking whichever number is highest. Keep repair materials to hand, because a unique cannot be replaced at a crafting table when it wears out.