A few people above said "...have the (pet) attack...". I think that earns you less Honor.
Quoting from Stratics...
"Gaining Honor:
You can gain Honor by engaging in honorable combat with monsters or NPCs. You can do this by double-clicking the Honor icon on the Virtue gump and targeting an appropriate opponent. You will face your opponent, bow to them, and speak the words, “I honor you.”
You then must defeat your opponent in an honorable fashion.
Honorable combat is defined as:
* Allowing your opponent to damage you first.
* Engaging in one-on-one combat.
* Not using ranged weapons, unless you stay in the same spot where you honored your opponent, or you only damage your opponent while adjacent to them.
* Not allowing your pets or summoned creatures to help you during the battle.
* Avoiding the use of poison.
To engage an opponent in honorable combat, your opponent:
* Must be one that you can perform negative actions upon.
* Must be at full health.
* Must not already be honored by a nearby player.
* Must be close to you, in your line-of-sight, and have a clear path to you."
After a lot of badgering from tamers, I remember a Dev commenting that the exact same rules of Honorable Combat apply to tamers and their pets.
Every time one of the rules of Honorable Combat is broken, the amount of Honor gained is reduced. So tamers start out at a disadvantage. Unless you let the Honored critter attack you/pet, you reduce the Honor gain even more. There was also a rumor that using more than one pet reduced the gain even more.
