In a saucepan over medium high heat, cook the sugar, until it starts to melt on the bottom. Stir continuously until the sugar sticks together and forms clumps/shards.
Stir slowly until all the clumps melt and sugar has durned a golden brown color. Reduce heat to medium.
Stirring continuously with one hand, add the butter with the other. Because the butter is colder than the caramel, the mixture will bubble and sizzle quite a bit.
Once all the butter has completely melted, still continuously stirring, slowly pour in the coffee and creamer. The mixture will sizzle even more than before, but just keep stirring carefully and quickly.
Add salt and continue slowly stirring for another minute.
Remove the pot from heat and let the caramel sauce cool completely before using.
(Caramel sauce can be made ahead of time and stored in an airtight container at room temperature.)