This paper addresses a problem well-known amongst practitioners of the Split-Hopkinson Tension Bar method: attaching a flat test specimen made from sheet material to the cylindrical input-and output bars. To date, slotting the bar ends and gluing the specimens into these ends with high-strength adhesives is the gold standard. However, this approach is not universally applicable because some materials are difficult to bond, and the adhesion surface is limited by the bar diameter, meaning that only small width specimens can be tested. In contrast, the hitherto published mechanical clamping mechanisms typically introduce excessive additional mass into the Split-Hopkinson system which detrimentally affects wave propagation and thus causes errors in the stress-strain signals. We circumvent this problem by designing a mechanical clamping device which has the same acoustic impedance as the bar material and is suitable to securely attach specimens with a width larger than the bar diameter. The benefits of our new clamping device are demonstrated by reporting tensile stress-strain data for Polycarbonate at high strain rates. The data is free from unwanted oscillations and enables accurate determination of dynamic strength and stiffness.