Remixed BamBam's very useful mini bit handle to work with 4mm micro-sized bits.
The first plate has the perfect size on my printer. It will be slightly too tight at first, work a bit in and out a few times to loosen it up. It's better this way than it starting off too loose.
I also included versions with tiny 0.06mm adjustments to the hole size in case the first one doesn't work for you. If you need to adjust further I'd suggest scaling all 3 at the same time to find the right size, a tiny 0.03-9mm adjustment can make a big difference.
The key setting for size precision is “outer walls first”.