Fill an ovenproof bowl with water; this is so you can submerge the bottom of the saucepan in water if caramel starts to burn.
Insert a small stick into the stem end of each apple. Set the apples aside on lightly buttered parchment paper, waxed paper or Silpat sheet.
Combine the sugar, corn syrup and water in heavy-bottomed, medium-sized deep saucepan. Stir with a wooden spoon to blend well. Cook over medium heat. Don't stir until the syrup becomes a deep, golden amber color.
Remove from the heat. Using a clean wooden spoon beat in butter. Then, stir in the cream. Add the salt.
Dip the apples, one at a time, in the caramel, swirling and tilting to coat them completely and evenly. Return the apples to the prepared paper to cool and harden.