In order to get an exact copy of the Kurviger Route, I recommend exporting the Track. However, some navigation devices handle the Route or Waypoints better, so you really need to try which works best for you. Adding additional waypoints is a good idea to keep your navi closer to the Kurviger route.
If you are using an Android device, I recommend using the Kurviger Pro app. If you are using an iOS device, I recommend using the Scenic app.

Kurviger can export route files as GPX and ITN. Newer TomTom devices can import GPX and ITN, older devices can only import ITN (and possibly GPX2ITN, see below). If you require the route to be identical to your planned route, you should choose the GPX track. If you want to change some route options or waypoints, the ITN file is recommended. Mind you, your TomTom will recalculate the route if you choose ITN, therefore it might differ from your planned route, you can choose to generate additional waypoints to help your TomTom device to stay on the planned route. You can find nice TomTom Rider specific tutorials on www.goldwingfahrer.de, the website has a Google Translate feature built in. Especially interesting might be the tutorial about transferring routes to a TomTom Rider (with images) and an explanation of the differences between route and track (ITN vs. GPX).

You can also use the Kurviger app to transfer a route via Bluetooth on the go. Just plan a route using the app and export it. Connecting your smartphone with your TomTom Rider differes between TomTom Rider 4XX and TomTom Rider 5XX.
Using a TomTom Rider 4XX, go to the main menu, click on "My Routes", this should enable the Bluetooth feature, if not, please review your handbook or check the settings.
Using a TomTom Rider 5XX, go to the main menu and then "Bluetooth"->"Add device"->"Add telephone". You might need to scroll to see the note about the MyDrive-App, click on the question mark in the bottom-right. Scroll down and choose to connect without the MyDrive-App.
Connect your Smartphone to your TomTom, on your Android go to "Settings"->"Bluetooth". Now you can transfer the exported route file to your TomTom, a Filebrowser app can help you to find the route file and to share it via Bluetooth. Select the file, click on "Share"->"Bluetooth" and select your Rider. You have to accept the transfer on your Rider as well. Now you should be able to select the new route in your Rider in the "My Routes" screen.

Older TomTom devices (e.g. Rider-Urban or Rider 2013) allow you to transfer GPX files using the so-called GPX2ITN. Here your TomTom will convert a GPX track automatically to an ITN. Export the GPX track from Kurviger and connect your TomTom to your computer. Copy the downloaded GPX file to your TomTom device into the folder GPX2ITN. Disconnect the TomTom from your computer. Turn your device on. When the conversion has finished you can load your route. In the main menu, tap "Manage itinerarie" and "Open". More details can be found here and here.

First, you have to export the route from Kurviger (I recommend you to add additional waypoints). In iTunes, with a connected iPhone, click on the iPhone symbol, go to "Apps" and scroll to the bottom. There you will find Apps that allow you to exchange data with. Choose Be-On-Road and import the route that you just downloaded from Kurviger. From Be-On-Road choose "Destination" and then "Routeplanner". Use the "Load" symbol (the box with the arrow) on the lower edge to import the route. Choose the route and load it. Now you should see the waypoints of the loaded route. You can delete selected waypoints by touching them and choose delete in the dialog. Thanks to Marcus for providing these instructions.

You should have installed DropBox and IITNConverter. If you have never saved a route as favorite in Sygic, you should first save a route as favorite, before continuing. In Sygic, setup DropBox and log into your DropBox. Plan a route using Kurviger and export it as Gpx-file using the route option and additional waypoints. You have to convert the Gpx-file using ITNconverter to the .itf format (Sygic GPS Navigation). In DropBox go to Apps -> Sygic All regions -> res -> itinerary and copy your route to that path. Use your iPad or iPhone and open Sygic. On the top right next to "Search", you have to click on the small flag. You will see a menu, choose favorites. The route should be listed there. Important unfortunately, the route will not be displayed by the saved name. There will be either a duplicated route or the route will be named by the start or end point of your route. Thanks to Achim for providing these instructions.

You should have installed CoPilot on your Android. You need the pro version of CoPilot for importing routes. Export your itinerary from Kurviger using the Waypoints option and the .trp Format (I recommend you to add additional waypoints). Connect your Android device to your computer. You should see your Android device from within your file explorer. Copy the downloaded .trp file to your Android device into the folder SD card\Android\data\com.alk.copilot.*\files\EUsave, whereas the asterisk marks the actual installed version of CoPilot. Start CoPilot and go to Route -> Plan or Edit Route -> Load -> choose the route.

Some navis like the TomTom Rider can receive routes via Bluetooth (see the TomTom Export for more details). If your satnav uses a microSD card, it might be possible to insert the sd card into your smartphone, transfer the route onto the microSD card and put it back into the satnav. In addition, you can use USB OTG. Not every smartphone supports USB OTG, please check if yours does. You need a USB OTG adapter (should be reasonably cheap at most electronic stores). Connect the adapter to the USB port of your mobile device and to your navigation device. You should be able to see your navigation device in a file explorer on your mobile device (e.g. ES File Explorer). Copy a downloaded route file to your navigation device as you would do from your computer. We tested this with a Zumo 550 and a TT Rider 400.