During operations, river and tidal hydrokinetic turbines encounter changes in flow direction that decrease their performance. Evaluating hydrokinetic turbines in yaw conditions contributes to estimating turbine performance, power stability, and power delivered to the grid. Water tunnel tests using a 19.8 cm diameter horizontal axis model turbine in yaw operation show the performance reduction using three designs: no shroud, a convergent-divergent shroud, and a diffuser shroud. Experimental results obtained at three Reynolds numbers of 1.38 × 105, 1.77 × 105, and 2.17 × 105 show that the output power decreases in off-axis flows for all designs investigated. The reduction is initially negligible up to a 10° yaw angle, but then increases with increasing the yaw angle. The convergent–divergent shroud experiences significantly less performance loss compared to the other two designs. The maximum performance loss of the convergent-divergent shroud design is 6% on average for the Reynolds numbers investigated. Based on the experimental results and in analogy to the linear momentum theory cosine cubed rule, we propose new cosine relations for shrouded turbines in yaw operations. Depending on the shroud's geometry, the maximum power of a shrouded turbine decreases either with the cosine or the cosine squared of the yaw angle.