Idea : Honor gives 5 Ip from your own
I figured then it'd be meaningful when someone gives, without giving more Ip/RP/skin etc which Riot apparently rejects. 5 Ip sounds like little but that's keeping in mind people may want to honor multiple. And no one's gonna give 5 ip every game without meaning it anyway, because it adds up.
The other neat thing related to is that they could make it so you get the IP gathered every 35 games (not 35 honors, games), if you get sanctioned before that you don't get the IP until your sanction is done, if you continue you may never get access to. So that's an incentive to be decent, without taking their gifts.
When it comes to the honor count and badges, I'd prefer if there were a single honor type, one for teammates and one for opponents, Honorable Teammate and Honorable Opponent. That's because as people pointed out, it's easy to have the descriptions not even match the person's actual activity, a person with teamwork badge is told they're a leader, and a person honored friendly commonly qualifies as a good player as well but can only be given one or the other. I also think it'd be more convenient not having to confirm every time, only first time with it informing it would give 5 IP. Maybe it being a toggle, with you selecting and being able to undo it by clicking again, with the system applying your decisions only after you close post game window.
Then I think they could look cooler than they do now, because they have to really look cool if you want people to at least like them as much as ward skins. Maybe there could be themed ribbons, like for the factions ig, Noxus, Demacia, Frejlord (etc), and for each champion with it being usable on any other champion. It could end up conveying what champ is your main if it's used without matching the champ selected. It could have 2 variants, one for teammate badge, and one for opponent. Like if the champ is Lulu, you get some sparkly purple ribbon with either pix symbol instead of the gem for teammate, and whimsied enemy symbol for opponent.
I think it would probably look nicest as a border instead, but I'm not sure if they'd prefer they remain ranked reward only. Maybe the visual part could be tied in with ranked by making it so people can unlock one border of their choice if they finish on 2nd and 1st division bronze, 2 borders if they're in silver, 3 in gold, etc. (or just gold above only) But they'd have to be among most honored players as well. It shouldn't be something like 5% though, but more like top 30%, there would be a lot of diff borders so even if more common it's special and reflects the person's preferences in champions, factions or simply art taste. So.... the first requirement is that they're top 30% honored in ranked, then they can unlock an amount reflecting their ranking.