The distinction between the high-magnetic field pulsars (HBPs, thought to be mainly rotation-powered) and magnetars (commonly believed to be powered by their super-strong magnetic fields) has been recently blurred with the discovery of magnetar-like activity from the HBP J1846–0258 in the SNR Kes 75. What determines the spin properties of a neutron star at birth and its manifestation as a magnetar-like or more classical pulsar is still not clear. Furthermore, although a few studies have suggested very massive progenitors for magnetars, there is currently no consensus on the progenitors of these objects. To address these questions, we examine their environments by studying or revisiting their securely associated SNRs. Our approach is to: 1) infer the mass of their progenitor stars through X-ray spectroscopic studies of the thermally emitting supernova ejecta, and 2) investigate the physical properties of their hosting SNRs and ambient conditions. We here highlight our detailed studies of two SNRs: G292.2–0.5, associated with the HBP J1119–6127, and Kes 73, associated with the AXP 1E 1841–045, and summarize the current view of the other (handful) HBP/magnetar-SNR associations.