Try earth.nullschool.net server to see the predicted RH values at the altitude of 250hPa in your area at the time. They correlate well with the occurrences of persistent contrails at least in Europe and North America. Here, for example, the "prediction" for California on April 20, 2016 at 21:00 UTC, which was a good day for contrails:
It correlates well with the satellite images of the day:
You can use earth.nullschool.net for real predictions, checking the predicted RH values for the next day or two, it generally works. I did it here a few times, the predicted values tend to change upon recalculation with the most recent data, but these changes are small. As in the weather forecast, the predicted persistent contrails may appear a bit earlier, or a bit later than the initial prediction.
I just found that you can stop the animation on the earthnullschool maps which makes for a less cluttered map. Click on the triangle next to Grid.
Incredibly beautiful clear skies today in N.E Australia not a contrail to be seen.