My question is in the title: how exactly do those honor badges work which show up on your profile when you're doing well?

I got 7 friendly, 4 helpful, 28 teamwork and 13 honorable opponent and still I got nothing while I have seen players with a badge who had less honor than me. How come...? And no, I don't trade or something, I got my score from random opponent.

the only known badge is the honorable opponent, you need 25 for that.

the others no one knows, coz you eventually get honored by your premade friends and you lose the count on them

i have every honour badge but, honestly i have no idea what the number is. someone before said that if you don't keep being honoured you lose the badge, i guess no one really knows.

I guess its 10 for helpfull, 15 for friendly and 15 for team work.

I've got 24 for team work and still haven't got a badge, so it must be more complex than that or I just simply haven't reached the target number yet.

if you are getting honored by your premade friends it counts as 0 lo

I got a honor badge/ribbon for teamwork, will check out how much honor I have and get back at ya. In a game atm.

I basically get honored multiple times every match so if that goes the same for you you prolly will get one too!

I got my honorable opponent badge at 27. I have 48 teamwork but still no teamwork badge and I never play premade so Im also guessing when some people in every game honor everyone their votes mather less etc.

It's not just about the number. The system is pretty complex, and only Riot really knows how it works.

You must bribe rioters to get it.