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. Here, we present Herschel PACS and SPIRE photometry at 70-500um 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 = 82K and mass 0.0031Msun; this is spatially coincident with thermal X-ray emission 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 90K with mass 0.0086Msun. Comparing the spatial distribution of the warm dust with X-rays from the ejecta and swept-up medium, and Ha 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 >0.07Msun 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 0.088(0.017)Msun for ejecta expanding into surrounding densities of 1(5)cm-3. The model predicts that silicon- and carbon-rich dust grains will encounter the interior edge of the observed dust emission at 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. ; Comment: 17 pages, 14 figures, accepted for publication in MNRAS, final version including corrected typos and references