Offering to do specific tasks is one of the best things that can be said to someone when they are sick. For example, instead of asking if there is anything that can be done, offer to bring them soup or dinner at a specific time.
Another option is to offer to drive them to a doctor's appointment or wait with them while tests are being processed. Offer to take their children to a sports practice or to school if they do not feel like driving. Also, if someone has a serious medical condition, offer them a shoulder to cry on or share a laugh.