The highest accuracy method for angle measurement employed at NIST (National Institute of Standards and Technology) makes use of an automated stack of three indexing tables--our Advanced Automated Master Angle Calibration System (AAMACS)--in conjunction with one of two possible instruments for small-angle measurement. The small-angle measurement system is usually an autocollimator, but we have also used a Fizeau phase-stepping interferometer in this role. We have performed numerous experiments to characterize the performance of the Fizeau interferometer for angle measurement. The two small-angle measurement systems are subject to a variety of potential errors when measuring imperfectly flat surfaces or imperfectly mounted artifacts, and we have quantified many of these sources of error. Potential errors of the Fizeau system, such as diffraction and various aberration effects, are small relative to potential errors associated with the measurement of non-flat artifact faces. Furthermore, when measuring the angle between imperfect surfaces, our two instruments implement slightly different definitions of the "average angle", and we might expect to see a significant difference in results from the two instruments. In actuality we have seen only very small differences when measuring typical artifacts.