I got the Nightingale Blade a while back and it wouldn't upgrade. I didn't care but I have realized that it's base damage is more than a daedric swords base damage. I have the highest level version. What do I do to fix this?
If you're playing on PC, you need to install the Unofficial Skyrim Patch. If you're playing on an Xbox, you can transfer the save to PC, improve the weapon and transfer the save back. If you're playing on a PS3, you're out of luck.
This happens because Bethesda failed to implement smithing improvements for some items. The Unofficial Skyrim Patch fixed it, here's the changelog entry that lists which items were fixed.
Fixed the following weapons and armor not being improvable at a workbench or grindstone: Amulet of Articulation (9DFF7/F6904/D/E/F/10/11) [yes, these amulets are actually armor and their internal name indicates that this is intentional], Diadem of the Savant (F9904) [also an armor amulet as previous], Dragon Priest Dagger (1C1FE), Drainblood Battleaxe (F82FA), Drainheart Sword (F71DD), Drainspell Bow (F82FC), Ebony Blade (4838F), Fine Armguards (86990), Gilded Wristguards (E84C1), Headsman's Axe (BE25E), Honed Falmer Sword (6F6FF), Honed Falmer War Axe (6F700), Jagged Crown (DA750), Keening (6A13C), Masque of Clavicus Vile (D2846), (Notched) Pickaxe (1019D4/E3C16), Scaled Horn Armor (1B3A4), Nightingale Blade (F6527) [this is the highest-level one; the other four could already be improved, and like the Nord Hero Bow this one had an entry but it was set up wrong, so was clearly intended], Shield of Solitude (9E023/10EB62/3/4/5), Shield of Ysgramor (E41D8), Shiv (426C8), Shrouded Cowl Maskless (5ABC4), Silver Sword/Greatsword (10AA19/10C6FB), Skyforge Steel Dagger (9F25D), Studded Imperial Armor (13ED8 - also 6 enchanted variants can now be improved), Supple Ancient Nord Bow (5D179), The Woodsman's Friend (22265), Tumblerbane Gloves (F5981), Ulfric's Bracers (6230B), Woodcutter's Axe (2F2F4) [the almost-identical Poacher's Axe could be improved], Worn Shrouded Armor/Boots/Cowl/Gloves (10EB5B/C/D/E) and Wuuthrad (956B5) [The justification for calling these omissions bugs are comments made pre-release and a loading screen that indicates that all weapons and armor may improved; to avoid arbitrary decisions of materials, magnitude or feasibility I did not add missing crafting options or perk keywords, nor change items that don't appear in the unmodded gameworld; if you use a crafting mod such as the Lost Art of the Blacksmith or weapon improvement mod such as WAF along with the USKP they will not conflict; ie multiple entries won't appear in the stations' menus]