The Bible says that believers will indeed judge angels.
Do you not know that we shall judge angels? how much more, things that pertain to this life? (1 Corinthians 6:3).
The judgment of angels is something that has been given to believers. Though humanity has been made a little lower than the angels in nature, those who have trusted the Lord will be given the responsibility of judging them in the age to come.
Nature of Judging
The nature of the judgment of the angels is not stated, but judgment does not imply condemnation. Since the good angels do not sin, there is nothing for which to condemn them. The judgment of angels most likely has to do with rulership in the kingdom. The Bible teaches that believers will be rulers over different aspects of the kingdom of God. Jesus made this clear in one of His parables.
"His lord said to him, 'Well done, good and faithful servant; you have been faithful over a few things, I will make you ruler over many things. Enter into the joy of your lord' (Matthew 25:23).
Faithfulness in small things, will allow believers to rule over many things. Angels will be included in this sphere of rulership.
Condemn Evil Angels?
What about the idea that believers will judge evil angels? Can this be what the passage is speaking about? As we search the Scriptures we find nothing that indicates that believers will stand in condemnation of the evil angels. At the Great White Throne judgment, the Lord is the one who will condemn all who are lost.
And I saw a great white throne, and Him that sat upon it, from whose face the earth and the heaven fled away; and there was found no place for them (Revelation 20:11).
Summary
The judgment of angels is something that has been committed to believers. The nature of the judgment will be one of rulership, not of condemnation. Redeemed believers will exercise authority over the angels in the ages to come. There is no scriptural basis that believers will stand in condemnation of evil angels.