Add the sugar and 1/4 cup water to a small/ medium saucepan and whisk over low heat until the sugar is all dissolved. Remove your stirring utensil. Then use a pastry brush dipped in a cup of water to brush down the sides of the pan so the sugar doesn't crystallize.
Turn the heat up to medium and bring the syrup to a boil. Without stirrring, let it boil, swirling the pan occasionally, until it turns a slightly dark amber-brown color and starts to smell a little caramelized. Carefully remove from the heat.
Then VERY carefully stir in the 3/4 cup of water. Watch out, the caramel will sputter quite a bit, so do it slowly. Once all the water is in, place the pan back over low heat and stir continuously until any caramel that siezed up is dissolved and the syrup is completely smooth.
Remove from the heat, stir in the salt, and pour into a clean jar or container. Let cool completely uncovered, then cover and keep in the refrigerator for up to 2 months. Add a couple teaspoons to your coffee and enjoy.
*Caramel can sometimes be a little tricky. If you don't cook it enough and the color is too light, you won't have that burnt caramel flavor. But with that said, the time in which it goes from amber-colored caramel to darker yummy burnt caramel to icky hard disaster caramel is quick, so once it starts turning golden brown, watch it like a hawk. (If you mess up, try it again. I guarantee with a little trial and error you too can master caramel.)
*If you do accidentally take the caramel too far and it turns rock hard and sticks to the pot, then to clean it more easily, just fill the pot with cold water, then boil the caramel off and wash the pot with soap and water.