Spintronic metal thin films excited by femtosecond laser pulses have recently emerged as excellent broadband sources of terahertz (THz) radiation. Unfortunately, these emitters transmit a significant proportion of the incident excitation laser, which causes two issues: first, the transmitted light can interfere with measurements and so must be attenuated; second, the transmitted light is effectively wasted as it does not drive further THz generation. Here, we address both issues with the inclusion of a high-reflectivity (HR) coating made from alternating layers of SiO2 and Ta2O5. Emitters with the HR coating transmit less than 0.1% of the incident excitation pulse. Additionally, we find that the HR coating increases the peak THz signal by roughly 35%, whereas alternative attenuating elements, such as cellulose nitrate films, reduce the THz signal. To further improve the emission, we study the inclusion of an anti-reflective coating to the HR-coated emitters and find the peak THz signal is enhanced by a further 4%.