The technology described herein is directed towards a cryogenic-stripline microwave attenuator. A first high thermal conductivity substrate such as sapphire and a second high thermal conductivity substrate such as sapphire, along with a signal conductor comprising one or more attenuator lines between the substrates form a stripline. A compression component such as one or more screws, vias (plus clamps) and/or clamps presses the first high thermal conductivity substrate against one side of the signal conductor and presses the second high thermal conductivity substrate against another side of the signal conductor. The high thermal conductivity of the substrates facilitates improved thermalization, while the pressing of the substrates against the conductor reduces the thermal boundary (Kapitza) resistance and thereby, for example, improves thermalization and reduces thermal noise.