Ni-Ti-Hf is a promising candidate for technological applications as a shape-memory alloy due to its increased transformation temperature between the austenite and the martensite phase as compared to pure NiTi. In this transformation, the energetics and elastic behavior of different crystallographic phases play a crucial role. We have determined the stable ground state phases of B19’ NiTi1-xHfx from a cluster-expansion approach based on density-functional theory calculations. It shows that the ordered ground states have only a small negative formation energy, i.e. there is only a small driving force for ordering. We have investigated the energetics of the ordered ground states, but also for the system with a random arrangement of Hf on the Ti sublattice, using the Coherent Potential approximation. For the investigated systems we have calculated the full matrix of elastic constants as well as averaged macroscopic moduli. We discuss ordering tendencies of Hf in NiTi1-xHfx and analyze the influence of Hf on the electronic structure of the system as well as its impact on the elastic behavior.