Laser triangulation sensors are one of the most commonly used optical sensors in dimensional metrology and quality control. This paper presents a method for simulating the laser speckle-induced measurement uncertainty, representing a major performance limitation of these sensors, as well as a method for reducing the influence of speckle on the achievable accuracy. To investigate the relation between triangulation angle and the resulting speckle-induced uncertainty, simulations are performed for three sensor geometries, revealing that a larger angle results not only in a smaller measurement range but also in a reduced influence of laser speckles and a smaller uncertainty. The accuracy of the simulation method is validated by measurements conducted with an experimental setup, demonstrating good agreement between the measured and simulated uncertainty values. To reduce the impact of speckles on the measurement accuracy, a diffuser mechanism is integrated into the optical path, reducing the resulting speckle-induced measurement uncertainty by up to 63%.