- The Premio Andersen, awarded by the Italian Children's Book Association, in 2000.
- The Premio Bancarellino in 2002.
- The Premio Cento in 2004.
- The Premio Elsa Morante Ragazzi in 2005.
- The Premio Strega Ragazze e Ragazzi in 2006.
- The Premio Gigante delle Langhe in 2007.
- The Premio Rodari in 2008.
- The Premio Letteratura Ragazzi in 2009.
- The Premio Andersen Award for Best Italian Author in 2011.
- The Premio Nazionale per la Letteratura Ragazzi in 2013.
In addition to these awards, Dami has also been named a UNICEF Goodwill Ambassador and has been awarded the Order of Merit of the Italian Republic.