Ask many photographers how to shoot in the harsh midday sun and they'll tell you either to supplement or diffuse your light or simply not to do it at all. This great video talks about how to embrace that light and get awesome shots with no additional equipment.
Coming to you from Manny Ortiz, this helpful video follows him as he does a shoot during the middle of the day with no reflectors, artificial lights, or the like. As Ortiz mentions, one of the best ways to take advantage of midday sun is to turn the model's face more toward it to even out the light distribution. Of course, this turns your model's face more upward. Depending on your height, you might find this a bit problematic when you're shooting. I personally like carrying a small step ladder to most of my shoots. Not only will this alleviate the aforementioned problem, it also offers you some different perspectives even when shooting normally. Another tip: if you have a model who's particularly sensitive to sunlight, have them close their eyes, and give them a quick countdown so they can open them just before you press the shutter and before they start to squint again.