Uber is still a rarity where I live in Berkshire, UK, so I can't readily try this out, but there's a new UWP in the Store dedicated to tracking and checking the cost of Uber rides. Perhaps you can comment once you've tried it in real life - how accurate is it?

From the Store description (sic):

Use UMeter to track how much your Uber cost while you're riding it.

• Detect your current location, check with Uber service, and show rider all the available services.
• Start trip, and complete the trip when you reach your destination; your Uber fee will calculate in realtime based on Uber rate at your location and service type rider choose.
• Tolls fee is not automatically include, as for the results, rider have to add it in manually.
• This is just an estimation, Uber final charges is the official

Some of the promo screenshots:

UMeter UWP is freeware in the Store here.

The developer does note: "It do have the issue that if the car goes into a tunnel, it can't correctly detect the distance, due to loss of GPS signal." Anyway, your feedback welcomed in the comments.