Cold outer debris belts orbit a significant fraction of stars, many of which are planet-hosts. Radiative forces from the star lead to dust particles leaving the outer belts and spiralling inwards under Poynting-Robertson drag. We present an empirical model fitted to N-body simulations that allows the fate of these dust particles when they encounter a planet to be rapidly calculated. High mass planets eject most particles, whilst dust passes low mass planets relatively unperturbed. Close-in, high mass planets (hot Jupiters) are best at accreting dust. The model predicts the accretion rate of dust onto planets interior to debris belts, with mass accretions rates of up to hundreds of kilograms per second predicted for hot Jupiters interior to outer debris belts, when collisional evolution is also taken into account. The model can be used to infer the presence and likely masses of as yet undetected planets in systems with outer belts. The non-detection of warm dust with the Large Binocular Telescope Interferometer (LBTI) around Vega could be explained by the presence of a single Saturn mass planet, or a chain of lower mass planets. Similarly, the detection of warm dust in such systems implies the absence of planets above a quantifiable level, which can be lower than similar limits from direct imaging. The level of dust detected with LBTI around beta Leo can be used to rule out the presence of planets more massive than a few Saturn masses outside of ~5au.