The angular diameters of α Orionis and ο Ceti were measured at a wavelength of 11.15 μm using the two-telescope Infrared Spatial Interferometer (ISI). Based on fitting the visibility data to uniform disk models, the diameter of α Orionis is 54.7+/-0.3 mas and that of ο Ceti at phase 0.90 is 47.8+/-0.5 mas. These diameters are the most precise ever measured in the mid-infrared, due in part to the addition of a 56 m baseline to the ISI, which provided sufficient resolution to observe the first zero in the visibility function of the stellar disks. Moreover, the effects of limb darkening and stellar hot spots are small at these wavelengths. Theoretically estimated limb-darkening effects indicate the actual diameters are approximately 1%+/-0.5% larger than the uniform disk approximation, or 55.2+/-0.5 and 48.2+/-0.6 mas for α Orionis and ο Ceti, respectively.