Like Cannot Cut Like

So you have a Cool Sword, An Axe to Grind, or another bladed or Energy Weapon that is absurdly sharp. Sweet! Now nothing can stand in your way, not even Ray Enforced adamantium-mithril alloy bulkheads! ... except for another, equally sharp weapon made of the same material, magical enchantment, technology or by the same Ultimate Blacksmith. Why? Well, maybe your Laser Blade's containment field is naturally blocked by your opponent's. Maybe they're both so impossibly sharp that the prospect of one cutting the other is like trying to make water wetter by splashing it with more water? Perhaps since both were Forged By the Gods, their nature as Empathic Weapons recognizes a sibling and refuses to harm it?

Whatever the case, neither weapon will scratch or dent, much less become a Wrecked Weapon. Only a direct hit on the opponent will end the duel... which is also likely to kill them unless your Implausible Fencing Powers are good enough to disarm them without, y'know, "disarming" them.

Needless to say, a character who thinks they have a Disc One Nuke in the form of their sword will be very unpleasantly surprised when facing an opponent who can even the odds. They may even get crushed if they've let their skills get rusty by relying on weapon's power. Such duels tend to prove suitably epic.

A Sub-Trope of Mutual Disadvantage, of the "mutual invulnerability" variety. Contrast Takes One to Kill One, when only like can cut like.

Anime and Manga

 * Battle Angel Alita: Last Order manga. Monomolecular wire can be stopped by a stick made out of monomolecular material.
 * In Black Butler, the Shinigami Death Scythes can cut through anything. Naturally, a Death Scythe can't cut through a Death Scythe.
 * Beam sabers in Gundam are made up of charged Minovsky Particles encased in I-fields. I-fields cannot block regular matter, so what allows beam sabers to cut through almost anything is the fact that hitting something with your saber is literally letting the superheated plasma of the saber eat through whatever you're trying to cut. When two beam sabers make contact, the plasma from both swords are making direct contact.
 * Beam shields, introduced in the second Universal Century, rely on the same general principle, they're basically a beam saber elongated into a wide plane that can be used to block attacks. Incidentally, if enough force is applied to a beam shield (or enough concentrated pinpoint power in the case of the Variable Speed Beam Rifle), it's possible to collapse it and hit the target behind it.
 * In Guyver, high frequency swords can't cut other high frequency swords, and when two high frequency weapons come into contact with each other, they make a deafening shriek.
 * Played straight in Shaman King, in that only Oversoul weapons can beat other Oversoul weapons (and Oversoul armor), but subverted when you get a character savvy enough to straight-up break their opponent's weapon, dispelling the Oversoul immediately.
 * In Naruto, Sasuke can channel lightning through his sword to give it incredible cutting power as well as inflicting paralysis, but both effects are cancelled out when clashing with one of Killer Bee's sword also enhanced (albeit differently) by lightning.
 * In Outlaw Star, Gene's caster shells could be blocked by firing another caster shell into them.
 * In Samurai Seven, the daito that the Samurai use can cut through anything from wood to Humongous Mecha...except other daito.
 * Gourry's energy blade sword in Slayers is eventually tested against another weapon that was created by the same people. When the two energy blades meet, they shriek.
 * Not only did they shriek, but they actually began to fuse together, and the energy released began to open a door to another dimension, wherein dwelt the god-killing Dark Star.

Film

 * The energy discs in Tron and Tron Legacy can cut through programs like butter, but will rebound off each other harmlessly..
 * Lightsabers in Star Wars have this property, along with the ability to reflect blaster bolts. Only a small set of non-saber weapons can effectively parry them.
 * According to ancillary materials, Sith lightsabers have properties that can occasionally cause the blade they are clashing with to deactivate. This explains why Obi-Wan's lightsaber flickered when he fought Vader in A New Hope.
 * More ancillary materials give you the Barab ingot crystal. This crystal, when inserted into a saber, gives it the ability to occasionally flicker and pass through a blocking lightsaber without destroying it.
 * The "reflect blaster bolts" property was touched upon in a novel, wherein an alien race was able to defeat Jedi because their blasters (permanently set to stun) had a different frequency. Lightsabers could be tuned to reflect these blaster bolts, but then they were rendered moot against regular blasters.
 * In X2: X-Men United, Wolverine and Lady Deathstrike both have the adamantium claws/fingernails. Likewise, in the Wolverine movie, Wolverine faces Weapon XI, which has an adamantium katana.
 * Also in X Men Origins Wolverine, William Stryker shoots Wolverine in the head with adamantium bullets (which is kinda justified, as a bullet, which is really fast, could have more impact than a blade). Doesn't kill him, but it does give him amnesia -- presumably the shock of the impact gave him severe brain damage and his Healing Factor couldn't piece all his memories back together.

Literature

 * Shardblades in The Stormlight Archive can cut through any non-living substance except other Blades and Shardplate as easily as swinging them through the air (they pass straight through living flesh without leaving a mark, but kill the victim anyway).
 * In the Incarnations of Immortality series, the highly magical Red Sword wielded by War cannot cut through Chrono's hourglass.
 * In Harry Potter, Harry's and Voldemort's wands behave quite strangely when they try dueling each other, due to the wands being "twins", having feathers of the same phoenix as their respective cores.
 * Averted in Michael Moorcock's Melnibone series; early on, Elric, armed with the runeblade Stormbringer, faces his cousin Yyrkoon, armed with Stormbringer's "sister" Mournblade. As the battle progresses, Elric slowly masters Stormbringer, which has a will of its own; conversely, Yyrkoon allows himself to fall under Mournblade's control, with the result that Stormbringer and Elric neatly overpower Yyrkoon and Mournblade... casting Mournblade into hell, or at least another plane. That part's never really explained clearly.
 * The titular Sword of Truth has been known to cut through any weapon or armor - except for one case when a similarly enchanted blade is encountered.
 * Averted in Sergey Lukyanenko's A Lord From Planet Earth with the planar swords. While a planar (or monoatomic) sword cuts anything, it's similar to a lightsaber in this regard in that it passes through like knife through butter. When two planar swords meet, one will always cut through the other. Which one is determined by the angle of impact and the sharpness of each blade. This completely changes how people fights with these weapons. So no Blade Locks here. Unlike lightsabers, anyone can use a planar sword given sufficient training, and you can get them anywhere, although they're only produced on one planet.

Tabletop RPG

 * Shadowrun. To stop monofilament attacks (e.g. a monofilament sword), wear armor/clothing with monofilament threads woven into it.
 * Nicely averted in Warhammer 40,000 where Power Swords and Monofilament swords will destroy each other if their edges cross. Both will nicely cut through a regular sword, too.

Video Games

 * In Sword of the Stars, Mesonic Torpedoes will go through all Deflector Shields except for Meson Shields.
 * In Super Robot Wars Original Generation, one of the very few things that can stop Sanger Zonvolt's Colossal Blade is another Colossal Blade, wielded by his Evil Twin.

Western Animation

 * When Samurai Jack first meets the Scotsman, he's surprised to find his nigh-invulnerable sword cannot as much as scratch the Scott's similarly-enchanted weapon. The two spend the entire day fighting, and only succeed in exhausting themselves.
 * When asked what made his sword special, the Scotsman replied "Celtic runes". This implies that his claymore, like Jack's katana, is endowed with magical properties, by gods or otherwise.
 * Inverted in the second Futurama movie, The Beast With A Billion Backs: The only thing that can cut or damage Electromatter (The substance that Yivo is made of) is more Electromatter. Otherwise, it's indestructible.

Real Life

 * Magnets: The sides with the same polarity will always repel each other.
 * Unless brought together by a greater force. Then colliding into each other both chips chunks off (reducing the magnetic power), and reduces the magnetic power further through the interaction of their respective fields.
 * This occurs in the sun. Stars basically start off as a collection of high energy protons, which collide with each other to create energy. The problem is, all protons are positive, and therefore, repel. And, under classical physics, we could conclude that there isn't enough energy to make the protons collide, making stars a physical impossibility. Luckily, with quantum physics, we now know that the protons can defy reality for a short span of time to make the sun reality.
 * Even more basic, the nucleus of an atom shouldn't be able to exist, considering it's basically a dense cluster of protons and neutrons (which add nothing). One of the four fundamental forces of nature, the strong force, keeps them that way.