They don't have to match.

 Bindings and thread don't have to match the quilt.  You can do what you want.  You can do a scrappy binding, pull a fabric that is in the quilt, do a two-colour binding.  It's all up to you.

These are quilts I just made up for the vet's office -- in case you missed the posts.  

Two colours!  I just picked them out at random and sewed them together.  Where they started, where they ended it just didn't matter.

This binding is a fabric that has been in the house for years.  I wanted it gone.  This was the end of it, so two strips finished off this little quilt with little to spare.

Cats come in all colours.  Some are black and white, some are orange.  Have fun with it.

Show them some love

Pull a fabric from the quilt and use that as a binding.

Or keep the theme going with the binding.  

The possibilities are endless.