So on the large demand of public, Microsoft has finally released an easy way to Backup Contacts and Messages on WP. Firstly it was only available to Lumia phones with SD card but now its available for phones without an SD card too.
This app gets installed within Settings and backs up your contacts (VCF format) and messages (XML format). This can be used for a later restore of contacts and messages on your phone. Basically the backup files get saved in a folder names “sms + contacts backup”. The app’s size is less than 1MB and reports say that it will be preinstalled with Windows Mobile 10. And yeah the app is released by Microsoft itself.
You can download this app from here: