"This is Hoshijiro, enemy craft down. He, he, he!"
-Ren Honaka, firing a rocket after Benisuzume-
Not much different from the standard Air-to-Air missile used by today's jet fighters and Anti-Aircraft missiles, the Anti-Gauna rocket is jet propelled, computer guided with an explosive warhead. Once locked on, it flies to the target, sticks into the ena, and explodes, taking off large amounts of Ena. Each Garde comes with four AGMs, they're mounted under the arms in tubes.
When Gauna 487 emerged and attacked the mining team, the revived Nagate attack his first real Gauna with a vengance. It's shapeshifting to look like his squad mate Eiko Yamano scared him, and he used two AGMs to blow off it's Yamano-like "face". The rockets took off nearly half of the "head." Once he was pulled away by Shizuka Hoshijiro, Norio Kunato destroyed pursuing Gauna Tentacles with an AGM.
After Hou Honaka's death at the hands of Benisuzume, Ren Honaka flew into a rage and pursued the specialized Gauna, firing Heigus beams and an AGM, all of which were easily dodged by the nimble, deadly Gauna.