In J.R.R. Tolkien's Middle-earth mythology, there are several significant swords with notable power and significance. Among them, two swords are often regarded as particularly powerful:

1. Andúril (Flame of the West): Andúril is the reforged sword of Aragorn, also known as Elessar. It is forged from the shards of the broken sword Narsil and given to Aragorn by the elf-smiths of Rivendell. Andúril symbolizes Aragorn's rightful claim to the throne of Gondor and is said to bring hope and courage to those who fight against the forces of darkness.
2. Glamdring (Foe-hammer): Glamdring is an ancient Elven sword, also known as the "Beater" or "Foe-hammer." It was originally crafted by the elf-smiths of Gondolin and later discovered by Gandalf in the troll's cave. Glamdring is said to glow with blue light when Orcs or other enemies are near and possesses the power to cleave through their ranks with ease.

Both Andúril and Glamdring have significant roles in "The Lord of the Rings" series and are associated with heroic characters. They are imbued with special qualities and are often depicted as highly effective weapons against the forces of evil.

It's worth noting that the power of these swords is largely symbolic and tied to the characters who wield them rather than possessing inherent magical abilities. The strength and significance of a weapon in Middle-earth often lie in the hands and hearts of those who bear them, as well as the deeds they perform.