Pulverized coal power plants are increasingly participating in aggressive load-following markets, therefore necessitating the design and optimization of primary superheaters for flexible operations. These superheaters play a critical role in maintaining the final steam temperature of the steam turbine, but their high operating temperatures and pressures make them prone to failure. This study focuses on the optimal design of future-generation primary superheaters for a fast load-following operation. To achieve this, a detailed first-principles model of a primary superheater is developed along with submodels for stress and fatigue damage. Two single-objective optimization problems are solved: one for minimizing metal mass as a measure of capital cost and another for minimizing pressure drop on the steam side as a measure of operating cost. Since these objective functions conflict, a multiobjective optimization problem is executed using a weighted metric methodology. Results from these optimization studies show that the base case design can violate stress constraints during the aggressive load-following operation. However, by optimizing the design variables, it is possible to not only satisfy tight stress constraints but also achieve the desired number of allowable cycles and adhere to the steam outlet temperature constraint. In addition, the optimized design reduces either the metal mass or the steam-side pressure drop compared to that of the base case design. Importantly, this approach is not limited to primary superheaters alone but can also be applied to similar high-temperature heat exchangers in other applications.