An expansion of the current honor system:
1 - Allow a short message that can be sent ("Great support" "Timely ganks" "Thanks for tips on items")
2 - Include checkboxes for dishonorable, but not reportable, behavior, (Did not respond to team communication, Did not show up for team fights, Kill stealing, Poor map awareness, Not paying attention, etc) - this is so that you can give critical feedback that you might not have time for during the heat of the game and which you may be too frustrated/angry to listen to from others during game.
The system would collect these comments and send them out at intervals, anonymously (so you can't just be mad at people who criticize you). This would also allow you to see, if, over time, there are things you consistently do well or which others consistently think you need to improve on.
Comments would be reportable also, in case they are used to send harassing/abusive messages.