Speech is a highly complex and multidimensional process, requiring precise coordination of muscular actions within the vocal tract. Disruptions or delays in speech motor control often lead to speech impairments. Recent advancements in markerless facial tracking technology enable the collection of objective measurements to assess these impairments. To obtain such photogrammetric measurements, a multi-camera network is employed, making accurate camera calibration essential. This paper examines the constraints applied during the calibration process. Two adjustment strategies were evaluated. The first, Independent Adjustment (IDP), performs self-calibration for each camera without introducing constraints. The second, Combined Adjustment (CMB), incorporates object space constraints by ensuring that object point locations observed from all cameras remain consistent. Given the cameras’ narrow fields of view, both IDP and CMB were tested with additional constraints related to the principal point offset. Each adjustment was executed under two conditions: fixing the principal point offset to zero or estimating it as part of the calibration. Results indicate that the choice of adjustment significantly affects the interior orientation parameters (IOPs). IDP with the principal point offset fixed to zero produced the most accurate outcomes. However, variations in IOPs had no meaningful impact on object space coordinates. These findings suggest that the simplest approach—IDP with the principal point offset fixed to zero—offers reliable calibration for multi-camera systems used in speech assessment. This streamlined method can be adopted in future applications to enhance efficiency without compromising accuracy.