I'll honour teammates for simply being nice people or for doing things in a way I'd not thought of. You can go 1/20/4, but if you are at least legitimately trying to do well and have a good attitude about everything, I'll consider honouring you. The reverse will also happen. You can go 20/1/14 and by using post-game chat to try to help the enemy learn for future match-ups will definitely result in an honour. Adding a bit of humour to chat will also probably get someone an honour. Puns of damage, joke comments relating to the game, etc. will not only make the game more enjoyable for everyone, it will also increase your own team's morale, leading to better cooperation and teamwork. I usually play support in solo-queue, and if I am given the ability to save a feeding teammate that at least has a positive attitude or a fed rager, 9/10 times I'll save the nicer person. It may not be the best idea as far as the current game goes, but it will at least reinforce the idea that nice in-game behaviour pays off. It's not that hard to be a decent human being, and if you are even the littlest bit helpful or friendly in a game, I will honour you for it.
I think the most honours I ever got and gave in one game was one where I was Vel mid, and the enemy Ahri DC'd at level 2. She came back when I was level 10. I offered to let her free farm until she hit 10 also. I stayed in mid to keep things from pushing, but just spammed emotes. Vel's attack-cancel animation is hilarious. Everyone on both teams honoured our call for peace, and left us alone. When she hit 10, things went back to normal, but that game was one of the best I've played in a long time. Everyone was really chill and chat was full of silliness.
Another weird one was where the enemy ADC's computer started glitching out HARD. I recognised the issue he was talking about, so walked him through the steps of how to fix things. That game I was Viktor, fixing a machine seemed fitting... My opponent left me alone while I was typing, so got an honour from me, and post-game I got 4 "Honourable Opponent" things.