Contact-Aided Compliant Cellular Mechanisms (C3M) are cellular structures designed with contact mechanisms integrated into each cell to provide stress relief. This paper addresses compliant cellular structures with curved walls and internal contact mechanisms. The use of curved walls in cellular structures tends to improve their global strain performance, and is beneficial for fabrication. The addition of contact mechanisms results in stress relief, allowing the cells to be stretched farther than they could without contact. Honeycomb cells with curved walls are modeled, and finite element analysis was used to calculate the maximum global strains for the non-contact and contact-aided cells. An optimization procedure was performed to find the cell geometries that resulted in the highest global strains. Strains of up to 32.4% and 19.7% are predicted for the optimized curved non-contact and contact-aided cells, respectively. The curved cells were found to be consistently capable of significantly greater global strains than the contact-aided cells with straight walls, making them ideal for high strain applications. Comparison of curved and non curved, non-contact and contact-aided cells shows that the curved feature of the cells results in a significantly greater improvement in global strains than adding a contact mechanism.