To specify the timeline, from the founding of the Roman Republic around 500 BCE to the fall of the Western Roman Empire in 476 CE.
What level of accuracy were they able to produce? How far did their maps extend? How detailed were maps? What equipment did they use to map the world? How did their cartographic skills compare to other civilizations at the time?
This is certainly an interesting question since only one map has survived antiquity, known as the Puetinger Map. My former Roman History professor is the go to guy for this subject so I'll point you in the right direction since all my knowledge on the subject comes from him. Book and high quality scans of the map itself.
Also here are some other articles on the subject: