We present high-resolution 890 mu m images of two 20 mJy submillimeter galaxies, SMM J123711+622212 and MIPS J142824.0+352619, obtained using the Submillimeter Array (SMA). Using submillimeter interferometric observations with an angular resolution of 2".5, the coordinates of these high-redshift sources are determined with an accuracy of 0".2. The new SMA data on SMM J123711+622212 reveal an unresolved submillimeter source offset to the east by 0".8 from an optical galaxy found in deep HST images, suggesting either a large galaxy with a dusty central region or an interacting galaxy system. The SMA image of hyperluminous (L-FIR = 3.2 x 10(13) L-circle dot) source MIPS J142824.0+352619 provides a firm upper limit to the source size of less than or similar to 1".2. This constraint provides evidence that the foreground lens is only weakly affecting the observed high far-infrared luminosity.