Here are some synonyms for "contemptuously":
* Scornfully
* Disdainfully
* Derisively
* Mockingly
* Disparagingly
Here are some examples of how "contemptuously" might be used:
* "He contemptuously dismissed her suggestion."
* "She looked at him contemptuously and turned away."
* "The politician contemptuously attacked his opponent's record."
Essentially, "contemptuously" indicates a harsh and dismissive attitude towards the subject of the action.