Some noble Houses have an ancestral weapon, usually a sword even if Celtigar's ancestor weapon is an axe. All of these ancestral weapons are made of Valyrian steel, except Dawn the ancestral weapon oh House Dayne that is made from the heart of a fallen star. Is it the only exception, or are there any other non-Valyrian steel ancestral weapons?
The Just Maid is the legendary sword of Galladon of Morne and it's said the Maiden herself gave him an enchanted sword.
"Ser Galladon was a champion of such valor that the Maiden herself lost her heart to him. She gave him an enchanted sword as a token of her love. The Just Maid, it was called. No common sword could check her, nor any shield withstand her kiss. Ser Galladon bore the Just Maid proudly, but only thrice did he unsheathe her. He would not use the Maid against a mortal man, for she was so potent as to make any fight unfair."
A Feast for Crows, Brienne IV
However, Master Hubert seems to believe that Galladon was a man of more recent times from Morne and if this is the case it's likely the sword stayed within the family.
Many of the folk of Tarth, highborn and low alike, claim descent from a legendary hero, Ser Galladon of Morne, who was said to wield a sword called the Just Maid given to him by the Seven themselves. Given the role that the Just Maid plays in Ser Galladon's tale, Maester Hubert, in his Kin of the Stag, has suggested that Galladon of Morne was no rude warrior of the Age of Heroes turned into a knight by singers a thousand years later, but an actual historic figure of more recent times. Hubert also notes that Morne was a royal seat of petty kings on the eastern coast of Tarth until the Storm Kings made them submit, but that its ruins indicate that the site was made by Andals, not First Men.
The World of Ice and Fire, The Stormlands: The Men of the Stormlands
We also have Lady Forlorn, although it's speculated as being Valyrian steel this is only in semi-canon sources so it's unclear as of yet. It is the ancestral sword of House Corbray.
The rest was a rout. Attacked from front and rear, the last great host of the First Men of the Vale was cut to pieces. Thirty lords had come to fight for Robar Royce that day. Not a one survived. And though the singers say the High King slew foes by the score, in the end he, too, was slain. Some say Ser Artys killed him, whilst others name Lord Ruthermont, or Luceon Templeton, the Knight of Ninestars. The Corbrays of Heart's Home have always insisted that it was Ser Jaime Corbray who dealt the mortal blow, and for proof they point to Lady Forlorn, reclaimed for House Corbray after the battle.
The World of Ice and Fire, The Vale