Aims. We investigated the degree of improvement in dark energy constraints that can be achieved by extending Type Ia supernova (SN Ia) samples to redshifts z > 1.5 with the Hubble Space Telescope (HST), particularly in the ongoing Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) and the Cluster Lensing and Supernova survey with Hubble (CLASH) multi-cycle treasury programs. Methods. Using the popular Chevalier-Polarski-Linder (CPL) parametrization of the dark energy w = w 0 + w a (1 − a) we generated mock SN Ia samples that can be projected out to higher redshifts. The synthetic datasets thus generated were fitted to the CPL model, and we evaluated the improvements that a high-z sample can add to improve the statistical and systematic uncertainties on cosmological parameters. Results. In an optimistic but still very achievable scenario, we find that extending the HST sample beyond CANDELS+CLASH to reach a total of 28 SN Ia at z > 1.0 could improve the uncertainty in the w a parameter σ wa by up to 21%. The corresponding improvement in the figure of merit (FoM) would be as high as 28%. Finally, we consider the use of high-redshift SN Ia samples to detect non-cosmological evolution in SN Ia luminosities with redshift, finding that these tests could be undertaken by future space-based infrared surveys using the James Webb Space Telescope (JWST).