Is there a cover that is designed for standing up the iPad 3 in portrait as well as in landscape orientation? I'm not talking about the Apple official Smart Cover. Something, possibly, in leather.
If you specifically want a case then the CaseCrown flip case is a good option: http://www.amazon.com/s?ie=UTF8&x=11&ref_=nb_sb_noss&y=19&field-keywords=casecrown%20Genuine%20leather%20vertical%20flip%20ipad%20case&url=search-alias%3Delectronics
However, if you really just want a stand then Twelve South makes the excellent Compass which does both portrait and landscape: http://www.twelvesouth.com/products/compass/gallery/
I have a Compass and I love it.
I also have a Twelve South Book Arc for my desk at home: http://www.twelvesouth.com/products/bookarc_ipad/gallery/
The Book Arc is heavy so you wouldn't carry it around, but it's great for a desk.
If you only want to place the iPad 3 in the vertical position, the first option is buy a stand for it. As you have asked for the case, then there are some cases that come with a stand. The crocodile leather plus stand case could be the right choice for you. It is built with leather and has a stand too. The black, white, and other colors are available. Hope this will helpful for you.