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.
The Moshi Versa origami case is great. It has a hard plastic back case and a thin cover that folds to allow the iPad to stand vertically (for portrait viewing, ideal for reading books) or horizontally (for landscape viewing, ideal for watching video). It also folds to make a 40 degree angle for typing.