A recently proposed model explains the rise in energy of the positron fraction measured by the PAMELA satellite in terms of hadronic production of positrons in aged supernova remnants, and acceleration therein. Here we present a preliminary calculation of the antiproton flux produced by the same mechanism. While the model is consistent with present data, a rise of the antiproton to proton ratio is predicted at high energy, which strikingly distinguishes this scenario from other astrophysical explanations of the positron fraction (such as pulsars). We briefly discuss important implications for dark matter searches via antimatter.