Nordic swords can be improved with a quicksilver ingot at a grindstone. They benefit from the Advanced Armors Perk, which doubles the improvement.
Unenchanted Nordic swords will begin to appear at level 25, and enchanted versions can be found at level 26.
A Nordic sword, as well as other Nordic weapons, can be obtained at any level by traveling to Solstheim, locating the Thirsk Mead Hall, and completing the quest "The Chief of Thirsk Hall." The weapons can be looted from the bodies of the former residents of the hall.