The Soft Gamma-ray Detector (SGD) is a Si/CdTe Compton telescope surrounded by a thick BGO active shield and is scheduled to be onboard the ASTRO-H satellite when it is launched in 2015. The SGD covers the energy range from 40 to 600 keV with high sensitivity, which allows us to study nonthermal phenomena in the universe. The SGD uses a Compton camera with the narrow field-of-view (FOV) concept to reduce the non-Xray background (NXB) and improve the sensitivity. Since the SGD is essentially a nonimaging instrument, it also has to cope with the cosmic X-ray background (CXB) within the FOV. The SGD adopts passive shields called "fine collimators" (FCs) to restrict the FOV to ≤ 0.6° for low-energy photons (≤ 100 keV), which reduces contamination from CXB to less than what is expected due to NXB. Although the FC concept was already adopted by the Hard X-ray Detector onboard Suzaku, FCs for the SGD are about four times larger in size and are technically more difficult to operate. We developed FCs for the SGD and confirmed that the prototypes function as required by subjecting them to an X-ray test and environmental tests, such as vibration tests. We also developed an autocollimator system, which uses visible light to determine the transmittance and the optical axis, and calibrated it against data from the X-ray test. The acceptance tests of flight models started in December 2013: five out of six FCs were deemed acceptable, and one more unit is currently being produced. The activation properties were studied based on a proton-beam test and the results were used to estimate the in-orbit NXB.