Gunpowder Empire
Harry Turtledove
 In the novel, Jeremy and Amanda Solter are two teenagers living in the late 21st century. Their parents work for Crosstime Traffic, a trading company using time travel to go back and forth from parallel versions of Earth to trade for resources to help sustain their version of Earth. One summer, the children work with their parents, going to Polisso - in our timeline a village in Romania with ancient ruins nearby, in the alternate timeline a major city of a Roman Empire that never collapsed. In the intervening centuries, the Romans advanced to the extent of inventing gunpowder - hence the title of the book - putting their armies on about 17th Century level. By 2100 they had not, however, gone through an industrial revolution and much of their social institutions, in particular slavery, remain as much as they were in earlier Roman times. North of the Roman Empire, a rival Lietuvan Empire has grown up, with occasional wars breaking out between the two. It is said that most of these wars would end in an exchange of border provinces. Romans consider the Lietuvans as "barbarians", though in fact the two have much the same level of technology and culture. When the youngsters' mother becomes sick, their father takes her back to their home time for treatment, expecting to come back in a few days - but the cross-time travel equipment suffers a break in link, stranding Jeremy and Amanda in Polisso just as the Lietuvan Army crosses the border, placing Polisso under siege. At the same time, the Roman authorities begin to grow suspicious of their trade mission and the origin of such items as watches and Swiss army knives which they offer for sale and which no artisan in the Empire can match.