A set of Ni-based single crystal superalloy aero-blade sections with electron beam physical vapour deposited thermal barrier coating (EBPVD-TBC) were used to investigate the role of substrate curvature on the microstructure and the residual stresses in the coating system. The residual stresses generated in the thermal barrier coating (TBC) and the thermally grown oxide (TGO) have been evaluated non-destructively by Raman spectroscopy (RS) and photo-stimulated luminescence piezo-spectroscopy (PLPS), respectively. In addition, residual stresses were measured in free-standing individual columns extracted from the TBCs for further understanding of the large Raman shift towards the tension side in the ceramic layer. For the TGO, three areas with varied substrate curvature were mapped by PLPS. These residual stresses are analysed as a function of the thermal exposure and the substrate curvature. Discussion focuses on the implications on how to correctly evaluate the residual stresses in EBPVD-TBCs based on Raman shifts and subsequently the role of substrate curvature on the degradation of the microstructure and evolution of residual stresses in this type of TBCs.