Nostalgia is a lot like viewing the past through rose-tinted glasses. In which case, Lewis's writing glasses must have been rose-tinted because Prince Caspian doesn't just envy the past through nostalgia—it straight-up worships it. Everything about Old Narnia is seen as a type of golden age for Caspian and his people, and their entire war is an attempt to make Narnia more like the Narnia of the past. They even receive help from the Pevensie children (ye kings and queens of yore). The characters who don't desire this past or who desire a different type of past are written as ignorant at best, or more commonly, as villains.
Even if he doesn't realize it, Miraz honors the past by his acknowledgment of Peter's legal power to challenge him to a duel.
The use of elements of our own world's past, such as the gods and creatures of Greek myth, helps connect the importance of the past in Narnia to the importance of the past in our world.