By resolution or just cause they mean that the result of any just war should entail reaching the objectives that served as the (just) cause for going to war in the first place. Thus, the primary parties involved must be held accountable until their mission is accomplished (i.e., blasting away and then letting the offending country pick up the pieces afterward is unacceptable), and those parties involved in the war must be prevented from taking advantage of the vanquished country's weakness and seeking additional (and unwarranted) gains.
Allman and Winright also believe that there cannot be a just peace without reconciliation. However, they are emphatic there call for reconciliation "is not about cheap grace or taking a 'forgive and forget' approach. [Rather] it involves acknowledgment of wrongdoing, admission of responsibility, punishment, forgiveness and perhaps amnesty. Ideally, reconciliation should lead to the return of the offending party to communion. The goal is justice tempered by mercy" ("When the Shooting Stops").
That said, they also believe that the guilty should be punished for their crimes. Such punishment, they argue, should should be carried out with transparency, proportionality and by authorities other than those who led the war, so that the war's victors are not seen as acting as judge, jury and executioner. This way those meting the punishment are seen as legitimate and the punishment itself as just.
Finally, Allman and Winright argue that the goal of a just war should also involve the restoration of the offending country to wholeness so that citizens of that country can live lives that are meaningful and dignified. Thus restoration involves practical matters such as providing security through policing and the rule of law, enabling the host government to promote the common good and provide basic services, fostering economic recovery, providing rehabilitation for those victimized by the war (and events that led up to it) and removing unexploded devices and munitions to prevent injuries in the future.
As noted above theorists are just in the beginning stages of hammering out what jus post bellum criteria might look like. Nevertheless, they are certainly food for thought as the U.S. seeks to extricate itself from Iraq and Afghanistan. We surely do not want to leave until we can assure the Iraqis and Afghanis a "just peace."