A typical mourning custom for first responders and public safety officers is the badge mourning band. As every department has specific guidelines regarding use of the band, I've included two links below that may offer insight.  
 
These bands are black elastic. The unstreched measurements are 5/8" wide, and 2 1/8" diameter.
 
For information on badge mourning band protocol:
Officer Down Memorial Page
National Fallen Firefighters Foundation