"Speak up and judge fairly;
defend the rights of the poor and needy."
Epilogue: The Wife of Noble Character
I think this verse just continues verse 8, talking about the need to speak up for those who cannot defend themselves. It also speaks of judging fairly.
People are good at saying, "It's not my place to judge." Excuse me. I think a better way of saying that would be, "It's not my place to condemn." Those are two different things.
We are to judge for ourselves whether a person is speaking truthfully or not.
We are to judge a person who has committed a crime.
We are to judge our brother who is in sin and warn him of his transgressions and the possible outcomes.
If we fail to judge, I think we allow for all sorts of evil to prevail.
This verse clearly says to judge, yet it says to judge FAIRLY. Don't claim that someone has done something that he has not. Don't accuse someone of sinning when she hasn't (read Job for some accusatory words, undeserved). Don't say that the preacher said something wrong in his sermon if you haven't taken the time to prayerfully read the Scriptures.
So....judge, but judge fairly.