Carbon Fiber Reinforced Polymer (CFRP) materials are used in aerospace structures due to their superior mechanical properties and reduced weight. Non-destructive evaluation (NDE) techniques are needed for such materials to detect and measure intra-ply matrix cracking and inter-ply delamination damage without harming or altering their initial configuration. The aim of NDE techniques is to use the composite material as a sensor itself, and to use its intrinsic material properties as measure of damage. Previous literature has shown that CFRP composites are electrically conductive in the fibers direction, and that the fiber-to-fiber contact due to waviness provides electrical conduction in the direction normal to the fibers. When matrix cracking or delamination defects are introduced in the composite, they break the fiber contact network, and this increases the local resistivity of the material. The Electrical Resistance Tomography (ERT) provides a NDE technique that uses these inherent changes in conductive properties of the composite to map its internal damage state. As opposed to other NDE methods, this technique allows the in-situ monitoring and detection on damage, which is particularly desirable for large and complex aerospace structures. This research investigates efficient numerical modeling techniques for inverse identification of delamination damage location and size in composite laminates using ERT based NDE. Identification of damage in composites requires solving the inverse problem that minimizes the difference between the model predicted and the measured change in resistance at specified electrode locations. The direct use of numerical finite element models of the laminate in the inverse identification is computationally expensive and it requires the development of accurate surrogate models. The use of Response Surfaces and Kriging approximations for single-response surrogate modeling is investigated in this work. Since the electrical resistance changes across the different electrode pairs for the given damage state could be correlated, this research also investigates the use of Singular Value Decomposition (SVD) in the identification of the principal components. The use of SVD for dimension reduction is also evaluated for the construction of accurate surrogate models.