One technique I have found that will help make you and your horse more confident in the show ring, try to make what you do at home harder then what the show will be. Make your jumps a bit bigger then the show will be, that way when you get there they will seem small and boost both you and your horses confidence. When your practicing on the flat ask for harder moves try to get flawless canter transitions from the walk or halt, try riding without stirrups. All these little things practiced on a regular basis will make everything you do in the show ring seem that much easier when you get there.
I have found many of my students have responded very well to this technique and are so relaxed and actually make comments on how small the jumps seemed or how easy the flat class was. Hope this helps!