If you want to backup your messages and contacts to your SD card and you are running Windows Phone 8.1 on your device then you should try this app named Contacts+Message backup which came to Windows Phone Store.
The app does what it name says i.e. it will back up all your contacts (in VCF format) and messages (SMS & MMS including attachments) to SD card (in XML format) for later restore to same or another Windows Phone.
Do note that if you install this app, it will appear in the Settings menu and not as an installed application i.e. you need to go in Settings of your Windows Phone to access this app. So what happens if you install this app in a Windows Phone without SD, well like it says it will go on to the Settings menu but when opened it will say that no SD card was found and subsequently wont back your stuff.
One of the known issue is that if you have a dual SIM device and you try to backup and further restore, it will go to message store of the first SIM.
So its a useful app but you need to careful about the warnings. Now if you still come under the category of people who wanna try it then you can follow on the link given in the source.