See some stats in post-game Honor screen to help determine who deserves it?
Quite often I haven't been keeping track of contributions/didn't look at scoreboard to see how well people are doing, I just play. Instead of honoring who actually may have deserved it most, I end up honoring whomever impresses me, even if their score was pretty bad. Like recently I think I honored the guy with the worst score, a Veigar, for making some sick stuns that helped me get a few kills, but in the end, other people I think deserved that honor looking at the statistics.
Maybe I haven't looked around enough on that screen, but you don't seem to have a way from what I recall to see who contributed the most/deserves that honor for whatever reasons (including support stats, to see if they healed/shielded/warded a lot/landed CC/etc.), you just have to already know by the time the game ends. If I happen to be split pushing a good amount for example, chances are I won't be watching the actions of my teammates the entire time. As a side note, I tend avoid honoring toxic people even if they do well, so having stats available would help determine who else might deserve it.
There's enough going on in a given game that I might not be able to make a fair determination of who deserves honor, without the post-game details available to be seen (even if I only have 30 seconds or so to look them over and decide, with the way the new honor system is currently designed). At this point, I mostly honor whoever I notice doesn't troll, doesn't feed, contributes in some way that impresses me (such as carrying with a decent attitude), doesn't tilt, or doesn't have a bad attitude/say anything to make it worse when others are causing problems amongst the team.
I don't know with what accuracy I'll be honoring the person who deserves it the most after a decent number of games, it'll just be based on what little I might notice during gameplay, while I'm concentrating on what I'm trying to accomplish. I know for sure people who cause problems in chat (I generally don't talk, and instead use pings, but sometimes I'll say something, hopefully to increase our odds of victory, or to share a little friendly banter; rarely I'll say something after being accused of something, with the hope of getting someone to stop complaining, perhaps due to a misunderstanding, and continue playing; I avoid it most times, since teammates tend to give up if an ongoing argument occurs), if I remember who they are, will not be getting honor from me regardless of how well they do. I have kept All Chat off for the last 2-3 months, so if they keep their nastiness there (and not on team chat), there's a good chance of those people getting honor from me.
I might regret it though once we hit the post-game chat, and I see the person I honored being toxic. I used to wait to see what people said before giving out honor in the old system (even if honor didn't mean much), if I thought someone deserved it. I'd also wait to see who might truly deserve a report, based on what they said in post-game chat, but I can still do that at least.