Cyclemeter is (appears to be) more of a cycle computer replacement (training tool). It does show a route on a map and your position relative to it. But there are lots of apps that do that. It's possible that the "elite" version ($5/year) does more but it doesn't seem to.

The story for Android is a bit better. There's a "cuesheet" app and there's a new app from ridewithgps (supposedly, ridewithgps has an iOS app in the works). Ridewithgps requires a subscription for navigation (you get other stuff too) for $6/month//$50 year.

Mapmyride has an app (not sure if it does turn-by-turn).

(There are a few apps that suggest they will provide turn-by-turn directions but either don't really or if they do, don't work very well.)