[en] The large order growth of string perturbation theory in c ≤ 1 conformal field theory coupled to world sheet gravity implies the presence of O(e-circumflex{-{1/g_s}}) non-perturbative effects, whose leading behavior can be calculated in the matrix model approach. Recently it was proposed that the same effects should be reproduced by studying certain localized D-branes in Liouville Field Theory, which were constructed by A. and Al. Zamolodchikov. We discuss this correspondence in a number of different cases: unitary minimal models coupled to Liouville, where we compare the continuum analysis to the matrix model results of Eynard and Zinn-Justin, and compact c = 1 CFT coupled to Liouville in the presence of a condensate of winding modes, where we derive the matrix model prediction and compare it to Liouville theory. In both cases we find agreement between the two approaches. The c = 1 analysis also leads to predictions about properties of D-branes localized in the vicinity of the tip of the cigar in SL(2)/U(1) CFT with c = 26. (author)