A computational certification framework under limited experimental data is developed. By this approach, a high fidelity model (HFM) is first calibrated to limited experimental data. Subsequently, the HFM is employed to train a low fidelity model (LFM). Finally, the calibrated low fidelity model is utilized for component analysis. The rational for utilizing HFM in the initial stage stems from the fact that constitutive laws of individual microphases in HFM are rather simple, so that the number of material parameters that needs to be identified is less than in the LFM. The added complexity of material models in LFM is necessary to compensate for simplified kinematical assumptions made in LFM and for smearing discrete defect structure. The first order computational homogenization model, which resolves microstructural details including the structure of defects, is selected as the HFM, whereas the reduced order homogenization is selected as the LFM. Certification framework illustration, verification and validation are conducted for ceramic matrix composite (CMC) material system comprised of eight-harness weave (8HW) architecture. Blind validation is performed against experimental data provided by the industrial co-authors of this paper to validate the proposed computational certification framework.