Cream shortening in a large mixing bowl; gradually add sugar, beating well. Add eggs, beating until well blended. Stir in orange rind and juice.
Sift together flour, baking powder, and salt in a medium mixing bowl; gradually add to orange mixture, stirring until well blended. Divide dough in half; cover and refrigerate 2 hours.
Roll one half of dough to 1/4- inch thickness on a floured surface, keeping remaining half chilled until ready to use; cut into 3-inch squares. Place a heaping teaspoon of mincemeat in center of each square. Moisten edges with water; fold pastry in half. Press pastry edges firmly together with tines of a fork.
Place on greased cookies sheets, and bake at 375° for 8 to 10 minutes. Cool slightly on cookie sheets. Remove to wire racks to cool completely. Repeat procedure with remaining dough and mincemeat.