Over the past 20-30 years, accuracy improvements in numerical coastal ocean models have been realized through greatly increased mesh resolution. High-resolution meshes reduce numerical dissipation and properly resolve physical processes in the nearshore. This increase in resolution has resulted in computationally costly simulations that have been made feasible alongside advances in parallel computing technology. However, the accuracy of the underlying numerical methods of these models has largely remained at second order. This means that while these models may produce results that are in good agreement with observations, the potential to improve their efficiency is limited. High-order methods offer a means to lower the computational expense of these models by leveraging their greater efficiency on a cost-per-accuracy basis. As a result, coarser mesh resolution can be used to maintain the same level of accuracy as today's state-of-the-art, high-resolution models at reduced cost. Despite these advantages, the implementation of high-order algorithms for realistic coastal problems is challenging. Given the complexity of these applications, several factors may negatively affect the solution accuracy, thus negating any expected efficiency gains. In the context of coastal ocean models, these challenges may be addressed by describing the domain geometry, bathymetry, and parameter fields with greater fidelity. This talk will discuss the implementation of iso-parametric elements and the creation of high-order bathymetry fields to create a fully-high order model domain. A simulation of the Galveston Bay area will be used to show that, together, a high-order algorithm and high-order domain description can provide solutions of similar accuracy to highly resolved, low-order models at reduced computational expense.