There is a vertical align property that I only recently realised is missing from Microthemer. I’m currently racing to meet my deadline of releasing the new UI by the end of May. But I will happily add the vertical align property to the release. But for now:
The logo has a parent link element with a top margin of 35px. You can target this element by double clicking the logo and then going to the “Inspector tab” of the advanced selector wizard options. Just click the up arrow once to move from the logo up to the parent link element. Then create the selector and reduce the top margin until it looks centred.
If you target the menu items and the search icon and set the line-height to 90px (the full height of the burgandy area) that should vertically align them.
ps the vertical-align property probably would work as you might expect for this problem anyway.