We present a new technique for designing a dual-band patch antenna with closely spaced bands of operation, whose response can be changed dynamically using a fluidic tuning mechanism. Using this technique, a dual-band tunable patch antenna operating at around 2.5 GHz is designed and fabricated using 3-D printing. Two oil-filled channels are placed in the substrate of the antenna along the nonradiating edges of the patch and filled with movable metal cylinders. As the cylinders are introduced underneath the patch, it starts to exhibit a dual resonant behavior with both resonances having a similar electric current distribution. The separation between the two resonant frequencies is a function of the relative position of the metallic cylinders underneath the patch antenna. As the overlap volume between the metal cylinders and the patch increases, the frequency of the first band, f1, starts to decrease and that of the second band, f2, increases. The maximum separation between f1 and f2 is achieved when half of the lengths of the metallic cylinders are underneath the patch. The prototype device designed in this work can achieve frequency ratios in the range of f2/f1 = 1.08-1.30. The antenna demonstrates similar radiation characteristics at both bands of operation.