Preheat oven to 350 degrees. Put the grated zucchini in a colander and toss with the salt; drain and squeeze dry.
In a large bowl, toss together the flour, baking powder, baking soda, cinnamon and nutmeg. Beat the eggs, sugar and butter and mix in the orange rind, orange juice and vanilla. Beat in the dry ingredients and stir in the zucchini.
Pour into a greased and floured 9- by 5-inch loaf pan (or four 4- by 21/2-inch pans). Bake 50 to 60 minutes or until a toothpick inserted in the center comes up clean (30 to 45 minutes for the smaller pans). Remove from the oven and allow to cool about 10 minutes before removing from the pan. Cool thoroughly before slicing or wrapping in plastic wrap.