Freeform optics, or optics with no axis of rotational invariance, provide optical designers more degrees of freedom, flexibility, and opportunity for innovation increasing optical performance and system integration while decreasing the form factor. Advancements in optical fabrication have enabled freeform surface manufacture with greater precision. Metrology instruments and techniques are needed to verify the performance of freeform optical surfaces and systems to keep up with design and manufacture. Freeform optics often have high slopes, no axis of symmetry, and a large departure from spherical, making traditional metrology techniques inadequate. This research was conducted to enable form measurements of freeform mirrors in the 250 mm class for a next generation three mirror anastigmatic (TMA) telescope complete with a statement of the measurement uncertainty to fill the gap in metrology of freeform optics. A flexible metrology instrument that could measure relatively large optics with customizable probe paths and sampling strategies was needed while maintaining the required uncertainty. Measurements were made using a Moore Nanotech 100UMM 4-axis coordinate measurement machine (CMM) with a probe path that allows for estimation of the thermal error and the possibility of compensation. A mathematical model was developed for the 100UMM using transformation matrices populated with the part and probe position vectors, probe displacement, machine carriage positions, geometric machine errors and probing errors. The model is used in geometric error compensation and a Monte Carlo simulation used for evaluating the task specific uncertainty. The geometric machine errors were measured for error compensation and the uncertainty in those measurements was used in the Monte Carlo simulation for task specific uncertainty evaluation of parts measured on the 100UMM. The mathematical model is also used to solve for the machine carriage positions to automate writing the machine language (g-code) for programming the probe path. A chromatic confocal optical probe was used to measure the reflective freeform optics. The Precitec chromatic confocal probe used is non-contact, has a large angle of acceptance, a 4.5 mm working distance and a 300 µm range. Initially, a point by point measurement strategy was used. To reduce overall measurement time for point to point measurements, the probe path was chosen using the traveling salesman approach. The traveling salesman problem (TSP) uses an algorithm to reduce the total distance traveled during the measurement in 3D space. Thermal characteristics of the 100UMM were evaluated using drift tests and temperature measurements. Drift tests are used to evaluate the amount of correlation between temperature and probe displacement. An environmentally controlled enclosure was installed around the 100UMM to stabilize the temperature of the ambient air, the high-pressure air going to the air bearings and the hydraulic oil for the hydrostatic bearings. The enclosure is designed to hold the metrology loop at 20 °C +/- 0.1 °C. Despite housing the 100UMM in an environmentally controlled enclosure, thermal error estimation and correction was necessary. Through probe path optimization and planning, thermal drift was estimated and corrected while the measurement time was reduced further decreasing the thermal drift. Limiting carriage movement while recording measurement data reduces the amount of thermal drift due to moving heat sources from the hydrostatic bearings and the drive motors on the carriages. The measurement time was reduced by a considerable amount by changing from a point by point measurement mode to a scanning measurement mode. By reducing measurement time, time varying errors including thermal error contributions are also reduced. The scanning mode, where the probe is moved over the surface of the part while recording the probe displacement, requires reading the machine scales directly and syncing the data acquisition of the probe displacement and machine carriage positions. The inability to sync the machine carriage positions and probe displacement at precisely the same time results in data age uncertainty. The data age uncertainty is reduced by limiting the carriage velocity, and number of carriages moving simultaneously. According to the guide to the expression of uncertainty in measurement (GUM) a measurement is not complete without a statement of uncertainty. A Monte Carlo simulation is used to evaluate the task specific uncertainty of parts measured on the CMM. The Monte Carlo simulation utilizes the mathematical machine model populated with the uncertainty in the machine and probe error measurements used for error compensation to evaluate the uncertainty in the best estimate of the surface being measured and specified measurands. To validate the metrology instrument and process, two half scale mirrors of third (tertiary) mirror in the AFRL TMA telescope was measured many times and in multiple setups for repeatability and reproducibility. The measurement result and statement of uncertainty were compared with the prescription and tolerances for acceptance. A spherical mirror made of glass was measured on a Fizeau interferometer and the 100UMM for a comparison of the measurement results after error compensation.