Here are some examples:
* She indignantly refused to accept his apology. (She was very angry and felt his apology was insufficient)
* He indignantly denied the accusations. (He was furious and insisted he was innocent)
* The crowd responded indignantly to the politician's remarks. (They were outraged by what the politician said)
Essentially, "indigantly" conveys a feeling of righteous anger or indignation.