The 29-year-old man is charged with setting fire to a plastic pallet and intentionally destroying a tent on March 2, the final day of the protest.
The woman, also 29, is charged with taking part in a riot on the same day. She was also charged with setting fire to a red petrol container, cushions, cardboard and other items on Parliament grounds.
Nelson District Court Judge Joanne Rielly granted interim name suppression for the pair until their next appearance. As it was their first appearance they entered no plea.