When framing a canvas you wouldn’t use a paper mat, instead you would use what is called a liner. A liner is a frame, placed inside the outer frame. Liners are available in many different sizes and shapes and are fabric wrapped. We have the fabrics samples in house and show you varying textures and colors of fabrics to best find what fits your artwork. Liners also serve much the same visual purpose as a mat, separating the work from its frame.
If you are looking for a more simple design then you can use what is called a floater frame. Floater frames have, in general, an L shaped profile and they do not have a lip to overlap onto the canvas. They come in a variety of sizes, colors and woods.