The [TM.sub.0] surface mode in an infinitely long parallel-plate waveguide filled with a double-positive (DPS) and epsilon-negative (ENG) metamaterial bi-layer is studied. With proper constitutive parameters and thicknesses of the two layers, the slow-wave factor (SWF) for such a parallel-plate waveguide can tend to infinity as the frequency decreases. A 2-D cavity based on the DPS-ENG bi-layer waveguide is constructed and studied to evaluate the radiation ability of its corresponding patch antenna. Based on the cavity model analysis of patch antennas, we show that good efficiency for broadside radiation of such a cavity-based rectangular patch antenna can be achieved when one layer of the cavity is shielded (or partially shielded) by PEC boundaries. Taking practical loss and dispersion into consideration, a miniaturized cavity-based rectangular patch antenna is proposed as an example. With the super-slow [TM.sub.0] surface mode excited in the bi-layer by a simple coaxial line feeding, the antenna has a dimension of only 0.107[[lambda].sub.0] x 0.129[[lambda].sub.0] x 0.045[[lambda].sub.0]. The patch antenna produces broadside radiation, and fairly good radiation efficiency is achieved. The PEC-Partially-Shielded-ENG-Cavity based rectangular patch antenna with a further miniaturization but reduced radiation efficiency is also discussed.