The apostle Paul makes a tantalizingly brief statement regarding the judgment of angels in one of his books. Disagreements inside the Corinthian church were not being handled correctly. Instead of members working out their differences between themselves (see Matthew 18:15 - 17), they were trying to resolve their issues by dragging each other before non-Christian courts (1Corinthians 6:1)! Paul mentions angels as part of his criticism and judgment of the church's behavior.
Paul first argues that Christians should be capable of handling disagreements by themselves since they will someday be granted judgment of the entire world (1Corinthians 6:2). He further extends his argument by stating, "Don't you (the Corinthians) know that we (Christians who are in the first resurrection) shall judge angels? How much more then the things of this life?" (verse 3, HBFV).
All those who died faithfully serving God will be resurrected during Christ's Second Coming to earth. They will be rewarded with a new spiritual body and life that will never end. They will also be given the privilege of ruling the earth with Jesus for one thousand years (Revelation 20:4, 6). Their human life of overcoming, coupled with the experience of ruling humans during the Millennium, will make them aptly qualified for the judgment of angels.
Will resurrected Christians judge all or only some of the angels? Though not stated in Scripture, it makes sense that believers would be a part of determining the fate of some or most of the demons. Additionally, based upon the principle that God will reward each Christian based on what they did during their lives (Matthew 16:27, 1Corinthians 3:8, Revelation 11:18), it is also possible such resurrected saints will help determine any reward righteous angels might be granted.
The Bible, however, does clearly state that God has reserved for himself the judgment of Satan. The great adversary of righteousness will ultimately receive what he justly deserves - eternal death in the lake of fire (Ezekiel 28:18 - 19, Revelation 20:10).
When might the judgment of angels take place? Although the Bible is silent regarding exactly when this event will occur, we can use what is known about God's plan to arrive at a likely date. Satan will receive his eternal punishment right after Christ's 1,000-year rule is completed (Revelation 20:7 - 10). God will then offer a full chance at salvation to countless resurrected humans during the period known as the Great White Throne judgment (also called the second resurrection, verses 11 - 13).
The Bible then seems to indicate that all those in the second resurrection (which is composed of humans, not angels) will be granted one hundred years of life in order to ultimately decide whether or not they are willing to obey God (see Isaiah 65:20). Those humans who are judged to have committed the unpardonable sin during this period, as well as those who previously did so, will receive the death penalty in the lake of fire (Revelation 20:14 - 15).
The final judgment of angels will therefore possibly occur during or immediately after the Great White Throne period. It is only after all incorrigibly wicked beings are taking care that God finishes his "clean up" of sin by creating a new heaven and earth (Revelation 21).