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.
These photos are dope, and the style and vibe certainly lends itself to the midday light working for it.
Also props to Manny for actually doing it here. I've seen a few other YouTube videos where the person talks about how to shoot in midday light, but the shadows in the examples clearly show they aren't shooting in the harshest noon lighting, or they cop out by shooting in shadow or with diffusion.
I did a pair of shoots a couple weeks ago in harsh overhead light like this. A couple of notes:
a) Hope your model doesn't show up wearing any makeup, or if so, that it's not an elaborate job. As you can see from the video, she or he will be sweating their @$$es off in that sun, and the makeup may / will run. So... bring a towel with you to have them pat themselves down. That sweat will be a nightmare to expose for and can appear as blown out high lights...
b) Manny is dead-on about angling their face into the sun. And he mentions, the light could blind them and force them to squint... so go with a closed eyes approach. Which can be a double-edged sword if you really want a traditional look of the eye. Get creative.
c) With the squinting, give the model a break, let them get out of the sun for a bit and compose themselves. Taxing work to sit in the sun for a shot....
d) Do a solid, and bring cold, bottled water. The model will appreciate it greatly.
e) Try to work quickly, as the sweating and eye strain can be much on the models.
I have mixed feelings on this time of day for a shoot. It's hard, but can result in good looks. I'd bring a reflector and someone or something to help hold it to get good lighting on the subject.