I have pondered what to write next for days, but "judging with right judgment" is relatively easy and I need not be long-winded here.
Keep love for the other person the main focus. Draw from Jesus within and speak the truth in love. The truth being simply what you observe in the material world. Keep condemnation out of your heart.
Some relationships include judgment on a regular basis: parent/child; teacher/student; employer/employee; policeman/citizen...you get the idea. All of these relationships are fruitful when the judgment needed simply observes the facts and uses these appropriately toward an outcome which is natural in the context of the relationship. Replicating this believer to believer is a supernatural experience from which we cannot shrink away. What the world sees and judges us by, and thereby "judges" our God is our love one for another.
Simply put to judge (analyze, objectify, discern, critique, estimate, categorize) without condemnation is a hallmark of love.