The enormous potential of additive manufacturing (AM), particularly laser powder bed fusion (L-PBF), to produce radiofrequency cavities (cavities) has already been demonstrated. However, the required geometrical accuracy for GHz 𝑇𝑀010 cavities is currently only achieved by (a) avoiding downskin angles <40°, which in turn leads to a cavity geometry with reduced performance, or (b) co-printed support structures, which are difficult to remove for small GHz cavities. We have developed an L-PBF-based manufacturing routine to overcome this limitation. To enable arbitrary geometries, co-printed support structures are used that are designed in such a way that they can be removed after printing by electrochemical post-processing, which simultaneously reduces the surface roughness and thus maximizes the quality factor 𝑄0. The manufacturing approach is evaluated on two 𝑇𝑀010 single cavities printed entirely from high-purity copper. Both cavities achieve the desired resonance frequency and a 𝑄0 of approximately 8300.