Here's a 3D printable badge holder for 3rd gen minis
 

Copypasta here from my Thingverse description... because the last time I made something for my Mini (a cell phone holder), BMW were *******s and sent in a bogus DCMA takedown on the page.

The existing badge holders seem to be made for the 1st/2nd gen. So I made this 3D printable holder. It also has the nice property of not needing to remove the grill to install the holder. Steps to install:

1. Buy a badge on Amazon or somesuch, should cost only about $9. Some of the badges are magnetic, but that isn't needed for this holder.
2. Print the holder in PETG or ABS (PLA will probably warp over time and doesn't do well with UV). Print front side down with supports on (the rough texture left from the supported area lets the glue bond better).
3. Attach to grill using two quick ties. After the ties are tight rotate them so they are fully recessed in their channel.
4. Apply some glue (I used Shoe-Goo) or epoxy to the front of the holder, then push the badge into the recess. Use blue tape to hold the badge until the glue dries.
5. If you ever need to remove the badge, there is a slot at the bottom of the holder where you can slip in a screwdriver and turn.

https://cimg6.ibsrv.net/gimg/www.nor...973559c3e6.jpg
installed
https://cimg8.ibsrv.net/gimg/www.nor...99910b2db0.jpg
as printed

Saw the link that shall not be named to the cell holder - any chance of throwing it in here?

basic goBadges holder attaches with a velcro strap and they have an alternate mount kit which includes 2 zip ties .... I suspect you could use your own!