How to reduce stress in pets?

Pets have souls or personalities and possess emotions and concerns just like we do. I have seen my pets undergo a process of grieving after bereavement resulting from death of a master or fellow pet. These are times of stress and the pet seems to have unanswered questions and might even go slow on food. I have also seen dogs being stressed by the prescence of many visitors in the compound who they are not used to. Because of their cautious nature, they expect the worst in such circumstances and seem to search their masters' faces for clues of reassurance. What is the best strategy to ameliorate pet stress?