Referring to the Roman Empire or its people:
* Imperial
* Latin (referring to the language)
* Classical
* Ancient
* Cae- (prefix often used in names like Caesar, Caius)
* Augustan (referring to the reign of Augustus)
Referring to the Roman Catholic Church:
* Catholic
* Papal
* Clerical
Referring to Roman numerals:
* Numeral
* Ancient numeral
Referring to the Roman alphabet:
* Latin alphabet
Referring to the city of Rome:
* Roman (this is still the most common and accurate term)
* Caput Mundi (Latin for "Capital of the World")
* Eternal City
Other possible synonyms:
* Imperial
* Powerful
* Grand
* Majestic
The best synonym for "Roman" depends on the specific context you are using it in.