The origin of interstellar dust in galaxies is poorly understood , particularly the relative contributions from supernovae and the cool stellar winds of low-intermediate mass stars . Recently , large masses of newly-formed dust have been discovered in the ejecta of core-collapse supernovae . Here , we present Herschel PACS and SPIRE photometry at 70-500 \mu m of the historical , young supernova remnants : Kepler and Tycho ; both thought to be the remnants of Type Ia explosion events . We detect a warm dust component in Kepler ’ s remnant with T _ { d } = 82 ^ { +4 } _ { -6 } K and mass \sim ( 3.1 ^ { +0.8 } _ { -0.6 } ) \times 10 ^ { -3 } M _ { \odot } ; this is spatially coincident with thermal X-ray emission and optical knots and filaments , consistent with the warm dust originating in the circumstellar material swept up by the primary blast wave of the remnant . Similarly for Tycho ’ s remnant , we detect warm dust at 90 ^ { +5 } _ { -7 } K with mass ( 8.6 ^ { +2.3 } _ { -1.8 } ) \times 10 ^ { -3 } M _ { \odot } . Comparing the spatial distribution of the warm dust with X-rays from the ejecta and swept-up medium , and H \alpha emission arising from the post-shock edge , we show that the warm dust is swept up interstellar material . We find no evidence of a cool ( 25-50 K ) component of dust with mass \geq 0.07 M _ { \odot } as observed in core-collapse remnants of massive stars . Neither the warm or cold dust components detected here are spatially coincident with supernova ejecta material . We compare the lack of observed supernova dust with a theoretical model of dust formation in Type Ia remnants which predicts dust masses of 88 ( 17 ) \times 10 ^ { -3 } M _ { \odot } for ejecta expanding into ambient surrounding densities of 1 ( 5 ) cm ^ { -3 } . The model predicts that silicon- and carbon-rich dust grains will encounter , at most , the interior edge of the observed dust emission at \sim 400 years confirming that the majority of the warm dust originates from swept up circumstellar or interstellar grains ( for Kepler and Tycho respectively ) . The lack of cold dust grains in the ejecta suggests that Type Ia remnants do not produce substantial quantities of iron-rich dust grains and has important consequences for the ‘ missing ’ iron mass observed in ejecta . Finally , although , we can not completely rule out a small mass of freshly-formed supernova dust , the Herschel observations confirm that significantly less dust forms in the ejecta of Type Ia supernovae than in the remnants of core-collapse explosions .