I used a glass for a pattern and then cut 1/4" around that. The blue line is disappearing ink. Love that stuff. Here's where I made my first error. The circle should have been about an inch or more larger.
I made a sandwich of backing wrong side up, batting, and quilt piece right side up and reinforced the seams of the vintage quilt top with a zig-zag stitch.
I had some blue bias binding left over from another project and began to stitch it in a 1/4" seam on the right side of the mat. It was about now that I realized this was not going well and the mat itself may not lie flat due to its size.
I folded the bias binding to the back and hand stitched the reverse side. As you can see in the photos below, I had almost cup shaped mats!
They're cute, but not even close to what I intended to make.
I actually tossed them aside and then decided to dig them out of the trash and make a mini wall hanging. I got some white ribbon and made a loop for the top and attached each circle to the ribbon.
You can see where I made a "fringe" of extra ribbon on the bottom for a touch of fun.
So, no mug mats for my friend, but a tiny wall hanging for me and some lessons learned. A 4" square of fabric does not make a good sized circle mug mat. I will try again for sure. I have three vintage quilt tops to play with. I can make bias binding in my sleep. And batting? I have enough to keep an army warm.
If you're interested in trying your own hand at mug mats/mug rugs, here are a couple links to patterns and one link to binding instructions. I'll have to read over these myself before I try to make another set!