 Nenzira imwe cheteyo muCheers spin-off Frasier, Grammer akarongedzerwa nguva dzose seMutungamiri Mukuru Anotungamirira muComedy Series panguva yose yekuratidzwa kunze kwe2003. Akakunda muchikamu ichocho cheMutungamiriri muna 1994, 1995, 1998, uye 2004. Akagamuchira mazita masere eGolden Globe Award nokuda kweBasa Rakanakisisa neMutambi muTerevhizheni Series Musical kana Comedy mumutambo wose wekutamba uye akakunda chikamu ichocho muna 1996 na2001. Grammer akahwina American Comedy Awards semutambi wechirume anonyanya kunakidza muTV Series Kutungamira Basa muna 1995 na1996. Grammer akakunda Screen Actors Guild Award sechikamu chevashandi ve Frasier muna 2000. 