I have found a way to initially show no results when a view loads, but if I want to display a specific value if nothing is found, that's a different story. One instance that you would want to do something like this is when you're making a distributor or representative locator. In this case, if no results are found, then you want to display the corporate office's contact information.
I am assuming you have selected the fields you want to display, filtered how you wanted, and exposed what filters you want the user to use.