A method and clamping apparatus for securing a substrate within a substrate carrier during an ultrasonic mounting process. The clamping apparatus may include a substrate carrier having a top plate and a bottom plate, the top plate and the bottom plate forming a cavity dimensioned to hold a substrate. A clamping plate is positioned on a side of the top plate opposite the bottom plate, the clamping plate having an opening aligned with the cavity and a pair of clamping members, each of the pair of clamping members extending toward a center of the opening and through the cavity such that the clamping member presses portions of the substrate exposed through the opening against the bottom plate. The method may include providing a clamping plate having an opening configured for alignment with a cavity formed in a substrate carrier and mounting a pair of resilient arms to the clamping plate.