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Single emitters in solid state are great sources of single and entangled photons. To boost their extraction efficiency and tailor their emission properties, they are often incorporated in photonic nanostructures. However, achieving accurate and reproducible placement inside the cavity is challenging but necessary to ensure the highest mode overlap and optimal device performance. For many cavity types -- such as photonic crystal cavities or circular Bragg grating cavities -- even small displacements lead to a significantly reduced emitter-cavity coupling. For circular Bragg grating cavities, this yields a significant reduction in Purcell effect, a slight reduction in efficiency and it introduces polarization on the emitted photons. Here we show a method to achieve high accuracy and precision for deterministically placed cavities on the example of circular Bragg gratings on randomly distributed semiconductor quantum dots. We introduce periodic alignment markers for improved marker detection accuracy and investigate overall imaging accuracy achieving $(9.1 \pm 2.5) nm$ through image correction. Since circular Bragg grating cavities exhibit a strong polarization response when the emitter is displaced, they are ideal devices to probe the cavity placement accuracy far below the diffraction limit. From the measured device polarizations, we derive a total spatial process accuracy of $(33.5 \pm 9.9) nm$ based on the raw data, and an accuracy of $(15 \pm 11) nm$ after correcting for the system response, resulting in a device yield of $68 \%$ for well-placed cavities.