Detailed numerical simulations of detailed combustion systems require substantial computational resources, which limit their use for optimization and uncertainty quantification studies. Starting from a limited number of CFD simulations, reduced-order models can be derived using a few detailed function evaluations. In this work, the combination of Principal Component Analysis (PCA) with Kriging is considered to identify accurate low-order models. PCA is used to identify and separate invariants of the system, the PCA modes, from the coefficients that are instead related to the characteristic operating conditions. Kriging is then used to find a response surface for these coefficients. This leads to a surrogate model that allows performing parameter exploration with reduced computational cost. Variations of the classical PCA approach, namely Local and Constrained PCA, are also presented. This methodology is demonstrated on 1D and 2D flames produced by OpenSmoke++ and OpenFoam, respectively, for which accurate surrogate models have been developed.