Honour is calculated by the resource cost of your units versus the resource cost of the enemy units. So the combined value of your lost units versus the combined value of the enemies lost units. Whoever loses the least in value will get the honour. Also the more honour you have the harder it is for you to gain if the enemy has very low honour and vice versa, if you have low honour its harder to give it to a player with high honour.
Honour dictates the heal rate to your troops and if you can raise the enemies honour up high enough you can effectively kill their troops while keeping your losses to a minimum. To raise honour the opposite is true, you have to attack your enemy killing as little of his troops as possible. This can be done in a number of ways and the most effective way is to send as small an amount of troops as you can. Many factors within the enemies defence will determine how much honour you give the enemy.
Knowing how to lose honour when both attacking and defending is an invaluable skill. You must always try to have your honour at 0. They key is making sure to always be constantly bringing it down with small attacks if you have low honour. On occasion, when a massive force of players attack you unsuccessfully, you can be stuck with 100s of millions of honour. Cases like this require a mix of techniques to bring it down.
The best practice to losing honour is to find a player with 0 honour and dump it on him, when he is fairly high move onto another player with as close to 0 as possible.
Using mech waves against an enemy in attack will almost certainly lose you honour even when you win, if you lose a few. The reason being they cost so much the unit value of a mech wave compared to a city full of infantry can be massive.
A big problem can be losing honour if you have no city teleporters and there are no hostile cities close.
There are a few different ways of doing it:
Wage War without Decoration
This stratagem can be won fairly often from the wheel of fortune and drops 10% of your honour. Its best used when you have high honour (20 million or more), and using it 10 times should drop over half your honour. However there is a cool down of 6 hours between using it so it can take days to get its full effect.
Many people will state that spam waves of 1,000 infantry, horse combos is the best way to dump honour but there is a far more effective way using cataphracts.
The basis is simple...
If you have say 20 million honour, find a player with 0 honour and send at first waves of 100 cataphracts. You can dump up to 100,000 honour a wave if the player only has abatis and archer towers on his walls and a high troop count. You should only get 10% heal on these waves. When your honour drops and the players honour rises you will notice that you will progressively dump less honour and when you get to a stage where you are only dumping 20,000 honour per wave you move onto the next step.
Start sending 200 cataphracts per wave, this should bring you back up to dumping 100,000 honour per wave, also your heal rate may slightly go up to 20%. As before your honour dumping will get progressively lower and again when your are only dumping 20,000 per wave move on and send 300 cataphracts per wave.
Keep repeating, 400, 500 etc up to 2000 per wave.
You can move millions in no time using this method. Some players will send 100,000 cataphracts at a player to dump honour and will lose about 10 million, but using this method you can dump 5 or 10 times that.
NOTE: As stated before honour is based on the combined resource cost, so fill the load vacancy with resources(preferably stone because it costs so little), also you want very low level heroes (level 1 - 20) with no gear equipped. You want your cataphracts to kill as little of the enemies troops as possible, preferably none at all.
There is a little known way of dumping honour in defence that i recently came across. Defensive trebuchet are very costly units, and have the maximum range (5000) meaning they will always fire at the start of a battle. If the enemy tries to send very small spam waves at you and you have a large number of trebuchets on your walls, you will actually lose massive amount of honour, because when the trebuchet fire, it counts as them being lost, and because small spam waves have a very low resources cost and your trebuchets have a very high cost, you will lose honour and your enemy will gain a pile. These can also prove a very good distraction because if the enemy isn't getting a report and is basing how much he is killing by his honour going up, he will think he is killing your troops when in fact he is being dumped with honour.