certificate of a negative COVID-19 test result taken within 72 hours
certificate proving a negative test result for COVID-19 that was conducted within 72 hours
People coming into Japan, including Japanese nationals, cannot enter the country without proof of a negative coronavirus test taken within 72 hours of departure.
日本語のに比べてちょっと長い表現になりますね。
certificate of a negative COVID-19 test result
certificate proving a negative test result for COVID-19
(コロナの)陰性証明(書)
certificateは証明書という意味ですが、証明のままであればproofもOKです。
例えば、
People coming into Japan, including Japanese nationals, cannot enter the country without proof of a negative coronavirus test taken within 72 hours of departure.
日本人を含む全ての入国者は、出国前72時間以内の陰性証明が無いと日本に入国できません
ご参考になれば幸いです。
アメリカ合衆国 
