The paper reports on the functional properties and microstructure of polycrystalline Ni-Mn-Ga-Hf high temperature shape memory alloys, in which different amounts of Hf up to 4 at.% are added in substitution of Mn and Ga, while the nominal Ni content is kept constant. The increase in the amount of Hf promotes a decrease in the valence electron concentration (e/a), tetragonality (c/a) of the martensitic unit cell, and martensitic transformation temperatures, as well as a significant decrease of the transformation hysteresis. The non-modulated tetragonal martensite, typical of Ni-Mn-Ga high temperature shape memory alloys, is formed in all the alloys studied here, though the alloy with 4 at.% of Hf also contains a small fraction of modulated 14M martensite. Hf addition improves the thermomechanical response of the alloys under compressive stress up to 300 MPa and leads to nearly closed cycles with minimal irrecoverable strain and low hysteresis (8 K) for the alloys with 3 and 4 at.% of Hf. These alloys also demonstrate excellent stability under repetitive thermal cycling and little change upon aging at 870 K. A second phase rich in Hf and Ni starts to precipitate at 1 at.% of Hf addition and its volume fraction experiences an abrupt and progressive increase for higher Hf contents. The structure of the second phase looks like the usual f.c.c. γ phase reported in other Ni-Mn-Ga-based alloys, but it has a double lattice parameter. Two structural models based on the A6 face-centered tetragonal unit cell with space group I4/mmm (No. 139), equivalent to the double f.c.c. lattice, are proposed for this new phase.