Dual drive gantry machines are widely used in industry for manufacturing. However, the non-synchronised movement of the dual drive may lead to deterioration in contouring accuracy, and traditional control architectures commonly used in machining cannot explicitly bound the contouring error to meet a desired tolerance. In this paper, we propose a model predictive control architecture based on switched linear time invariant control-oriented models, that is able to guarantee a two dimensional contouring tolerance in the presence of uncertainty arising from imperfect drive synchronisation. To develop the controller, we introduce a high-fidelity model for the dual drive gantry machine and identify its parameters using data from an industrial machine, and systematically reduce it to a control-oriented model. The performance and computational tractability of the proposed approach is demonstrated using high fidelity simulations.