A character has contracted some sort of unpleasant illness? If a cleric isn't at hand, you can use the following simple mechanic:
Each day, the character gets a % chance equal to his/her Constitution score to shake off the effects of the illness. For example, a character with a 9 Constitution would have a 9% chance every day.
Receiving some sort of medical attention (typically costing about 1 gold piece per day) gives an extra roll each day.
Characters with a saving throw bonus against poison may add the bonus to their constitution score.