the NoFan size makes it impossible to find any closed case that would fit it when placed on that motherboard.
What about something large, like the Cooltek/Rosewill/Jonsbo W1 ?
The reason why I don't expect any closed case to fit this motherboard with the NoFan mounted on it, is because there is not enough clearance around it.
This is how the NoFan would look like on top of the ASRock Z97E-ITX:
I used 183mm as the diameter of the NoFan, and made pixel measurements given the standardized locations of the motherboard and socket mounting holes. The photo is the one used by ASRock on their product page, and shows a little bit of distortion on the vertical features, but it's spot on when comparing items at the motherboard height level. Because of that, the heatsink circle has to be compared with the motherboard edges, and not with the vertical I/O connector features.
The NoFan overhangs the top of the motherboard by ~39.23mm, which might seem a lot, but there are cases which can fit that. I did pixel-based measurements on the Thermaltake Core V1 and Corsair 250D, and they are ok. These cases even fit the 147mm height of the cooler, even though they claim to fit only up to 140mm. And they have a top window which I can remove, so that I can passively cool the CPU thanks to the ventilation holes in the side panels.
But the problem is the overhang on the motherboard shield side. The NoFan needs an additional ~4.14 mm. Unfortunately, that's too much. The microATX spec says that the allowed distance from the motherboard edge till the chassis inner-side is 2.11 +/-0.25mm. That's only half of the 4.14mm I need. What can I say... "death by mm"!
Perhaps I did some mistakes, or perhaps the chassis manufacturers are making them with even worse tolerances and I would get lucky enough to receive one of them... or maybe I could enlarge the motherboard mounting holes by a few mm, till it all fits. I don't know, it looks like a lot of trouble. I'm also afraid the NoFan would touch the chassis and maybe that could short and fry something.
I am still not sure what to do about this.