Bed Bath and Beyond has this lovely little frame for $5.99 - take your 20% coupon with you! I found this in the store and was not able to find it on their web site. I was able to pop my square tile right in. It has a felt back with an easel - no hanging option.
Details: Siena Narrow Plain 3.5"x3.5" photo frame (Silver Color)
Below are some options I found at Michaels - take your 40% off coupon!
Photo Cube 3.5"x 3.5 inch - $3.99 each. Leave the square insert that comes with the cube in and slide your tiles in. You might want to put a little tape over one of the edges where it slides apart to keep it from accidentally coming apart if someone picks it up.
Packaging looks like this
Another option is this lovely frame that comes in white and black for $7.99. It is from their Hanging Collection and is a little bigger than the zentangle tiles at 4" x4 ", but works just fine if you flip the piece of paper that comes in the frame over and place it behind your tile! Images of front and back.
The final two framing options I found are magnetic photo frames. One is flexible and one is acrylic. I prefer the acrylic one over the flexible frame. Both are 3.5"x 3.5" and $1.99 each.