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A transition from cavity-backed coplanar waveguide (CBCPW) to rectangular waveguide using a short-circuited pin in conjunction with resonant sections of coplanar waveguide (CPW) and reduced height waveguide segments is presented. The proposed transition is designed with prismatic features in order to ease the fabrication process. An equivalent circuit model is developed to facilitate the design procedure and full-wave analysis is used to optimise the design. As an example a transition operating at Ka-band is designed and shown to have insertion loss of less than 1 dB and reflection below 10 dB over 9 of bandwidth for a back-to-back structure. To further validate the results a prototype transition at Ka-band for a standard WR-28 rectangular waveguide was fabricated and tested. The measured S-parameters of the prototype show a very good agreement with the simulation results.