My wife asked me to make some wood inlay refrigerator magnets with a bear motif that she could use as small party favors. In searching for magnets to use in their construction, I found the below 15mm x 2mm neodymium magnets on Amazon. They have just about the right amount strength for a fridge magnet; plus at only 2mm thick, they can be recessed in relatively thin material. I used a few drops of thin CA glue in round pockets cut in back side of the wood inlays, spayed some CA accelerator on the magnets themselves, and just dropped them in the pocket. Seemed to lock securely in place.
I used the 15mm x 2mm size -