The paper gives first quantitative estimates on the modulus of continuity of the spectral measure for weakly mixing suspension flows over substitution automorphisms. The main results are, first, a Hoelder estimate for the spectral measure of almost all suspension flows with a piecewise constant roof function; second, a log-Hoelder estimate for self-similar suspension flows; and, third, a Hoelder asymptotic expansion of the spectral measure at zero for such flows. The second result implies log-Hoelder estimates for the spectral measures of translation flows along stable foliations of pseudo-Anosov automorphisms. The Appendix explains the connection of these results with the theory of Bernoulli convolutions.