Have there been any duels where both duelers were wielding Valyrian steel?

Question

Valyrian steel is supposed to be a very good material to make weapons with, and to grant great advantage in combat. But have there been any duels where both duelers were wielding Valyrian steel?

Answer 1

Aegor "Bittersteel" Rivers vs Brynden "Bloodraven" Rivers

Bittersteel wielded Aegon's blade Blackfyre while Bloodraven wielded Visenya's blade, Dark Sister:

_{Note: In the above, I’m speaking of Aegon I Targaryen, first King of Westeros. Below the quote talks about Aegon Blackfyre, a son of the bastard, Daemon Blackfyre. Bittersteel is Aegor Rivers}

The rebellion ended at the Redgrass Field, nigh on a year later. Some have written of the boldness of the men who fought with Daemon, and others of their treason. But for all their valor in the field and their enmity against Daeron, theirs was a lost cause. Daemon and his eldest sons, Aegon and Aemon, were brought down beneath the withering fall of arrows sent by Brynden Rivers and his private guards, the Raven's Teeth. This was followed by Bittersteel's mad charge, with Blackfyre in his hand, as he attempted to rally Daemon's forces. Meeting with Bloodraven in the midst of the charge, a mighty duel ensued, which left Bloodraven blinded in one eye and sent Bittersteel fleeing.
_{The World of Ice and Fire, The Targaryen Kings: Daeron II}

A quote from The Sworn Sword indicates Bloodraven was indeed wielding Dark Sister at the time.

Six years ago in King's Landing, Dunk had seen him with his own two eyes, as he rode a pale horse up the Street of Steel with fifty Raven's Teeth behind him. That was before King Aerys had ascended to the Iron Throne and made him the Hand, but even so he cut a striking figure, garbed in smoke and scarlet with Dark Sister on his hip.
_{The Sworn Sword}

Although it was known that Bloodraven preferred his longbow made of weirwood, that would've been useless to him in a mighty duel against a prominent warrior.

---

Daemon I Targaryen vs Ser Gwayne Corbray of the Kingsguard

As indicated elsewhere, before the prior duel, and in the same battle, Daemon I Blackfyre duelled Ser Gwayne Corbray of the Kingsguard. Daemon I Blackfyre wielded Aegon's blade Blackfyre while Gwayne Corbray wielded Lady Forlorn, the ancestral sword of House Corbray.

Daemon was the Warrior himself that day. No man could stand before him. He broke Lord Arryn's van to pieces and slew the Knight of Ninestars and Wild Wyl Waynwood before coming up against Ser Gwayne Corbray of the Kingsguard.
_{The Sworn Sword}

Also, Bloodraven and Daemon Blackfyre wield swords of Valyrian steel, as does Ser Gwayne Corbray of the Kingsguard, also prominent in the battle.
_{So Spake Martin - Concerning the Great Bastards}

Answer 2

If we considered that Lady Forlorn is Valyrian steel, yes.

During the First Blackfyre Rebellion, a duel opposed Daemon I Blackfyre (wielding Blackfyre) to Ser Gwayne Corbray (wielding Lady Forlorn) of the Kingsguard.

Daemon was the Warrior himself that day. No man could stand before him. He broke Lord Arryn's van to pieces and slew the Knight of Ninestars and Wild Wyl Waynwood before coming up against Ser Gwayne Corbray of the Kingsguard. For near an hour they danced together on their horses, wheeling and circling and slashing as men died all around them. It's said that whenever Blackfyre and Lady Forlorn clashed, you could hear the sound for a league around. It was half a song and half a scream, they say. But when at last the Lady faltered, Blackfyre clove through Ser Gwayne's helm and left him blind and bleeding.
_{The Sworn Sword}

Answer 3

Probably yes, but only one (that we know about).

From this forum post:

In the first Blackfyre rebellion, Gwayne Corbray dueled Daemon Blackfyre, which was known to be the only duel in history where both combatants wielded Valyrian steel.

The description of the duel from The Sworn Sword:

Daemon was the Warrior himself that day. No man could stand before him. He broke Lord Arryn's van to pieces and slew the Knight of Ninestars and Wild Wyl Waynwood before coming up against Ser Gwayne Corbray of the Kingsguard. For near an hour they danced together on their horses, wheeling and circling and slashing as men died all around them. It's said that whenever Blackfyre and Lady Forlorn clashed, you could hear the sound for a league around. It was half a song and half a scream, they say.

Daemon Blackfyre's sword Blackfyre was Valyrian steel, and Gwayne Corbray's sword Lady Forlorn is confirmed in at least semi-canon sources to be Valyrian steel.