We present integral-field spectroscopic observations with the VIMOS-IFU at the VLT of fast (2000-3000 kms-1) Balmer-dominated shocks surrounding the northwestern rim of the remnant of supernova 1006. The high spatial and spectral resolution of the instrument enable us to show that the physical characteristics of the shocks exhibit a strong spatial variation over few atomic scale lengths across 133 sky locations. Our results point to the presence of a population of non-thermal protons (10-100 keV) which might well be the seed particles for generating high-energy cosmic rays. We also present observations of Tycho's supernova remnant taken with the narrow-band tunable filter imager OSIRIS at the GTC and the Fabry-Perot interferometer GHaFaS at the WHT to resolve respectively the broad and narrow Hα lines across a large part of the remnant.