Carbonfiber, we toured CR last summer and will be coming back there again this year. GPS device will be certainly helpful there, but mostly the routes were marked pretty well, so you won't have to look for the navigation suggestions all the time. We had a nice set of "Author" paper maps (that's a Czech bike production brand), it was well updated, at least for the Western part where we were wandering. If you change your mind and want to try a smartphone, then make sure you won't have same problem as i described earlier, turn off the network assistance, leave only true gps in navigation settings, and see how quickly you will get a correct position fix.

UPD. Just checked online maps for couple of places we found to be difficult. For example here, close to the entrance to Prague along Vltava river, in front of Vetrusice, there is a location where you literally have to get off the bike and walk because the path is too narrow with rocks on one side. On the end we did not go there since we had our babies with us and the trailer was simply too wide. Your tandem would make it though w/o problems. While it's still a part of the bike route, Ovi, google do not show the bike path at all. OSM cycle map shows the bike path but no information on the dangerous spot and only the paper maps had a proper warning.

My verdict would be: easy trips - bring whatever with you, feeling geeky - bring a smartphone, want to be sure - bring proper paper maps or any gps device (whatever has the right digital maps and the batteries) and proper paper maps.