On the surface, the success of a coaching relationship is decided based on a client achieving specific goals. Because the client is responsible for taking the action to achieve what they choose it is important to define their ownership in their success. The role of the coach is to provide the process and be a partner as taught during coaching certification. It is also important to dig deeper than the surface measurement of client goal achievement because sometimes goals change, and there are additional benefits to a coaching relationship. 
Success includes small successes along the way toward a larger goal as well as achieving the larger goal or desired outcomes. Learning a new skill, creating positive habits, and developing processes for creating future successes are additional benefits to a coaching relationship and part of measuring success.
When a client is firmly on track toward achieving their goals, they may choose to continue without regular coaching sessions. In that case, was the coaching successful? Yes!
During coaching certification, practice coaching includes exploring what the client wants and how they will measure the success of the coaching. This means before starting, a coach and client have a conversation to choose how the success of the coaching relationship is ultimately identified and measured. This is revisited periodically.
The client determines what they do want from the coaching relationship. If there is a sponsor, a process for measuring ROI is determined. In outlining how success is measured, consider the various possibilities and benefits. Provide for both quantitative and qualitative evaluation.
Remember to appreciate the opportunity to celebrate successes.
