We suggest an idea for miniaturization of cavities by utilizing a properly designed metamaterial thin surface inserted inside the cavities. This metamaterial surface is constituted by a thin dielectric slab on both sides of which “gangbuster” dipoles are printed. Inserting the thin slab inside a parallel-plate one-dimensional (1-D) cavity resonator has the effect of decreasing the resonant frequency. Placing the metamaterial slab at the center of a rectangular waveguide also lowers the cut-off frequency of the dominant mode of the waveguide. The corresponding dispersion curve exhibits a smooth transition from a fast-wave to a slow-wave regime and then asymptotically tends to the dispersion curve of the first TE surface-wave mode of the metamaterial slab. This suggests a natural way to conceive a 3-D compact cavity resonator by placing two perfectly electric conducting walls, a half of the wavelength of the slow-wave mode apart, inside the above rectangular waveguide. The analysis, performed by a circuit network theory and validated by a full-wave numerical analysis, provides simple formulas to predict the resonant frequency and the dispersion diagrams of these structures.