High-throughput fabrication of microstructured surfaces with multi-directional, re-entrant, or otherwise curved features is becoming increasingly important for applications such as phase change heat transfer, adhesive gripping, and control of electromagnetic waves. Toward this goal, curved microstructures of aligned carbon nanotubes (CNTs) can be fabricated by engineered variation of the CNT growth rate within each microstructure, for example by patterning of the CNT growth catalyst partially upon a layer which retards the CNT growth rate. This study develops a finite-element simulation framework for predictive synthesis of complex CNT microarchitectures by this strain-engineered growth process. The simulation is informed by parametric measurements of the CNT growth kinetics, and the anisotropic mechanical properties of the CNTs, and predicts the shape of CNT microstructures with impressive fidelity. Moreover, the simulation calculates the internal stress distribution that results from extreme deformation of the CNT structures during growth, and shows that delamination of the interface between the differentially growing segments occurs at a critical shear stress. Guided by these insights, experiments are performed to study the time- and geometry-depended stress development, and it is demonstrated that corrugating the interface between the segments of each microstructure mitigates the interface failure. This study presents a methodology for 3D microstructure design based on "pixels" that prescribe directionality to the resulting microstructure, and show that this framework enables the predictive synthesis of more complex architectures including twisted and truss-like forms.