Measurement and verification (M&V) function has been adopted in many energy efficiency (EE) programmes to quantify energy savings, identify new energy efficiency opportunities, improve EE programme design, and reduce EE programme performance risks. Budgetary constraints in EE programmes necessitate careful planning to minimise M&V cost whilst maintaining M&V accuracy. For this purpose, this study presents an M&V cost minimisation model to handle M&V sampling and modelling uncertainties cost-effectively. In the proposed model, the objective function is the total M&V project cost, which consists of M&V sampling cost, modelling cost, and overhead cost. The required M&V accuracy in terms of the 90/10 criterion is formulated as the constraints of this optimisation problem. Optimal solutions to the proposed model specify the required baseline model accuracy and sample sizes to achieve the desired M&V accuracy. The proposed model is applied to design an optimal M&V sampling and modelling plan for a traffic light retrofit project. Results show that the optimal M&V plan reduces the sampling cost by 42% and the total M&V cost by 11% against the solutions obtained by partial optimisation.