Drain the cherries, reserving the juice. Let dab the cherries gently with a paper towel so that they are as dry as possible. Set them aside on paper towels to continue to dry while you prepare the sugar filling.
In a medium size bowl, mix 3 cups powdered sugar, butter and ¼ cup cherry juice together. Add in the last cup of powdered sugar, ¼ of a cup at a time, until the mixture forms a soft dough. Refrigerate the dough for 20 minutes.
Roll the dough into 1 inch balls. Make small balls, about 1 inch in diameter. Flatten the dough balls between the palms of your hands, dusting your hands with powdered sugar if necessary. Fold the dough over the cherry to completely cover it, then roll it into smooth ball again.
Refrigerate the covered cherries for 20 minutes. Melt the Candiquik chocolate according to the directions on the back of the package. Holding the cherry by the stem, dip it in the melted chocolate and allow the excess to drip off. Place the chocolate covered cherry on a baking pan that has been covered with wax paper. Repeat with the remaining cherries.
You can use maraschino cherries without stems if you'd like. Use a fork to dip them in the chocolate, tapping off the excess chocolate.