The board's role: Support chief executive and evaluate performance
Supporting the CEO means backing up the CEO in public and addressing any concerns privately with tact and diplomacy.
Support comes from frequent and constructive feedback and for the board to take action if any Board member oversteps their bounds. This of course means that the board needs to recognize the boundaries of the relationship and delegate with authority. It also means, however, that the board does have a monitoring function that will build capacity and improve performance. Support also includes giving compliments for special effort and encouraging the CEO to seek professional development and personal renewal.
Performance evaluation should be privately conducted and based on an agreed upon purpose, method and frequency. Performance appraisal should be a positive and supportive experience for all. It should be an evaluation measured on results ad value to the organization. If done in the style of a partnership, you will maximize results.