To save partially melted butter, place it in a bowl with a few ice cubes and stir. In less than a minute, the butter will quickly cool and solidify to the soft texture you are looking for. Simply remove the ice cubes and proceed with the recipe. (The small amount of water that has melted into the butter won't affect the finished product.)
Keep in mind this method won't work with completely melted butter, so if you are looking at a puddle at the bottom of the bowl, it's best to save that butter for another use and start again with a fresh stick.
Do you have any tips or tricks for saving overly soft butter?