Give specific requirements for the art project. This gives the individual some rules to follow, although they can still create whatever they want, within the guidelines. This also helps you grade the material, despite your personal taste. If you wanted an abstract with certain colors used, and the individual followed the instructions, you can't grade them down just because you don't find it appealing.
Did the individual complete the fine art project on time? If not, then no matter how amazing the piece is, you have the option of deducting points as they had an unfair advantage over the other artists. Many art professors give a little leeway when it comes to this, as sometimes you can't always complete a project in an allotted time frame. But for contests, you need to stick with the set rules.
Have multiple judges if you are performing a fine arts contest. Sure, one individual is not going to like something you may love, but it helps offset any negative feedback you may have on a piece. Often times you may not know what you don't like (or do like) about the art project, so having another individual around is going to help.
Often times a sculpture or painting just isn't going to make any sense until the artist describes it. This description may make a world of difference. Perhaps once the artist points out key points in the painting you may finally understand what they were going after.
Don't judge art after a few minutes of looking. Instead, look over the work, take a break, then come back. With fresh eyes you are going to notice things in the world you never saw the first time