I really like your question. I think as we come to understand his character we can begin to strive to have those same characteristics in our lives. As we get to know him I think it becomes possible to measure how close to the savior we are getting. If we look at ourselves honestly we can measure our humility, compassion, patience, love, etc. I also think it's possible to recognize when we grow and change.
In my life it's also been the challenges and adversity I've faced that have helped me understand him better. Because of the pain I've had in my life I have much more compassion with those who suffer.I think when we encounter hardships if we keep his example in mind we will not only grow closer to him but become more like him. The choice when faced with our trials is to become bitter, resentful and cold or to forgive, grow and become like the Savior.
For me, no book has illustrated this greater than Les Miserables by Victor Hugo. Just reading about the Bishop of D's life and the changes made by Jean Valjean shows me that Victor Hugo must know the savior and the savior knows him. In his book when the abused Cosette goes out in the cold and darkness of night to fetch water she encounters the visually frightening former convict that is Jean Valjean and Victor Hugo tells us "The child knew no fear". I think children can sense Christ-like goodness, even those that have never experienced kindness. That's how I imagine the Savior to be. That's a characteristic I've seen in many who serve missions. That's one characteristic among many that I'm striving for.
Only thru becoming like the Savior do we have any hope of truly understanding his Will, the "will of the Father" and doing it.