Center an item with position: relative

I've got a menu that appears on hover over an absolutely positioned div. All of the menu items have to be relatively positioned because the absolutely div will appear multiple times on a page and will appear in multiple sizes in one instance.

How would I center multiple items with position: relative both vertically and horizontally when I won't know the the size of the parent div?

I know the position: absolute trick with negative margins, but this situation calls for something different.

Here's the code:

.OuterCase { 
  position  : absolute; 
  width     : 100%;  
  height    : 100%; 
  text-align: center;
}

.InnerItem  { 
   width  : 38px;
   height : 38px;
   display: inline-block;
}

I've got it to center the items horizontally; it's getting the vertical that's being a bit elusive.