It is well known that the motion of flexible vegetation leads to drag reduction in comparison to rigid vegetation. In this study, we use a numerical model to investigate how the detailed motion of kelp fronds in response to forcing by surface gravity waves can impact the drag exerted by the kelp on waves. We find that this motion can be characterized in terms of three dimensionless numbers: (1) the ratio of hydrodynamic drag to buoyancy, (2) the ratio of blade length to wave excursion, and (3) the Keulegan-Carpenter number, which measures the ratio of drag to inertial forces. We quantify drag reduction, and find that inertial forces can significantly impact the amplitude of kelp motion and amount of kelp drag reduction. Under certain wave conditions, inertial forces can cause kelp fronds to accelerate more quickly relative to the wave, which can lead to increased drag reduction and reduced wave energy dissipation. In some conditions, frond motion leads to drag augmentation in comparison to rigid fronds. Additionally, we discuss other features of kelp motion, such as the degree of asymmetry, and their relationship with enhanced drag reduction.