Judging Prophecy

Paul told the Corinthians to "Let the prophets speak two or three, and let the other judge. (1 Cor 14:29)," but I've always wondered how to do that.

How can one prophet judge another's prophecy without hurting their feelings or undermining their authority?

I gained insight through a story David Cartledge included in his book The Apostolic Revolution. Cartledge repeated a story originally told by Barney Coombs:

"I was sitting with a group of men in a council meeting. The evangelist with us brought a word of prophecy. The prophet turned to me and said, 'Barney, are we allowed to judge that prophecy?' Now we were like family around this table but you could have cut the atmosphere with a knife. I said, 'Be my guest.' He said, 'I don't think it was from God.' I turned to another man who is wise and also a prophet and said, 'John, what do you feel?' 'No,' he said, 'I don't think it was from God.' Then the man who was in charge of the business and also prophetic said, 'The prophecy we have heard is not from God, but the Spirit says that so and so did not share all he saw, and when he shares all he saw, it will be from God.' I felt goosebumps up and down my spine! I turned to the evangelist and said, 'Is that true?' And he said, 'Yes.' When he shared all that he had seen, all the men said, 'This is from God.' It changed everything."