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Spintronic terahertz emitters (STEs), based on optical excitation of nanometer thick ferromagnetic/heavy metal (FM/HM) heterojunctions, have become important sources for the generation of terahertz (THz) pulses. However, the efficiency of the optical-to-THz conversion remains limited. Although optical techniques have been developed to enhance the optical absorption, no investigations have studied the application of THz cavities. Here, to enhance the THz efficiency of STEs in a selected THz spectral range, FM/HM structures are realized on ultra-thin sapphire layers with metallic mirrors to create λ/4 THz resonant cavities. THz emission time domain spectroscopy of these STE/sapphire/mirror heterostructures, with sapphire thicknesses ranging from 110 µm to 25 µm, shows enhancement of the emitted THz field that fits the λ/4 cavity resonance with up to a doubling of the field in the spectrum, and in agreement with temporal simulations of the emitted THz pulse. By taking advantage of birefringent materials, we further show the potential of control of the polarization state of the emitted THz pulse. This work shows the potential of enhancing and engineering THz emission from STEs using THz cavities that can be controlled over a broad spectral range, which can be easily combined with optical cavities.