Using density functional theory calculations, we compute the edge energies and stresses for edges of SiC and BN nanoribbons, and the boundary energies and stresses for domain boundaries of graphene-BN superlattices. SiC and BN armchair nanoribbons show pronounced edge relaxations, which obliterate the threefold oscillatory behavior of the edge stress reported for graphene. Our calculations show small boundary stresses in graphene-BN superlattices, suggesting that such domain boundaries will not experience severe deformation. We have also found that the C-terminated and Si-terminated zigzag edges in SiC nanoribbons have different compressive stresses which results in different rippling behavior of these edges.