We propose a simple technique to form miniature optical circuits using microfibers embedded into a low refractive index matrix. As an example we demonstrate a silica microfiber knot resonator embedded in a fluoroacrylate polymer. Fabrication issues and initial experimental results are reported. We also present simulations aimed at understanding the current limitations to the Q-factor and the role of the embedding polymer refractive index on the Q-factor of future resonators. It is anticipated that using commercially available polymers high Q-factor resonators with radii as small as 100 micrometers can be made by this technique.