Rodoslovlje

1. Does my family have a coat of arms? 
No, most families in Serbia and the region were not armigerous due to the fact that the Ottoman Empire ruled the area. However certain families did get arms granted in service of the Austro-Hungarian Empire. In general most families don't have a coat of arms because it was a privilege held in medieval times by noble families. 

2. How do I make sure my family does or doesn't have a coat of arms? 
The only way to make sure is to do genealogical research. Genealogy is a science based on facts so by doing research you will be able to discover if your family did or didn't have a coat of arms. So before you start looking to get a coat of arms designed by someone make sure to do your genealogical research.