For some reason the Apple SDK does not provide a simple boolean Property where you can just disable it. A lot of solutions on StackOverflow requires you to set a background image and a shadow image to remove it entirely.
Digging through solutions a bit I found that these two ways seem to work pretty well.
So for the NavigationBar, what you do is traverse through all subviews to find the UIImageView which is the shadow and simple remove that from showing up. This is done as follows.
For the TabBar it is slightly different. It has a member variable, which is private, so you cannot get hold of it directly. However, using the SetValueForKey() method, which all NSObject's have, you can set that variable to true.