Amplify Shields, when filled, add a bonus amount of Amp Damage to the next shot (called an Amp Shot) fired from any projectile weapon, at a cost of a certain amount of shield damage (the shield's Amp Shot Drain). They are thus well suited to longer-ranged character builds where they can be allowed to recharge between shots and there is little risk of taking damage.
An Amplify Shield is essentially the opposite of a Roid Shield.
As rarity increases, the amp damage increase, while shield recharge delay and amp shot drain decrease.
The Bee – Legendary shield in Borderlands 2 with very low capacity but massive amp damage and zero amp shot drain.
Rerouter – Legendary variant of amplifying shield in Borderlands: The Pre-Sequel with a balance of stats offset in the direction of high increasing the amp damage. Heals the player for the amp drain amount when an Amp shot is fired.
As of November 14th, 2012, Gearbox released Patch 1.2.0 for Borderlands 2, Which added a balance that caused Amp Damage to be divided evenly among multiple projectiles rather than added to each, and added a bug fix so Amp Damage no longer applies to every round remaining in a thrown Tediore weapon, significantly reducing this shield type's former effectiveness for close-range character builds. Splash damage from explosions caused by a weapon's projectiles do receive the full amp bonus though, regardless of how many projectiles are fired, and guns that fire multiple projectiles but don't have a damage multiplier in the item card will have each projectile get the full amp bonus.
The common amplify shields is obtained randomly from any suitable loot source.