  We develop a complete set of tools for CMB forecasting, simulation and
estimation of primordial running bispectra, arising from a variety of curvaton
and single-field (DBI) models of Inflation. We validate our pipeline using mock
CMB running non-Gaussianity realizations and test it on real data by obtaining
experimental constraints on the $f_{\rm NL}$ running spectral index, $n_{\rm
NG}$, using WMAP 9-year data. Our final bounds (68\% C.L.) read $-0.6< n_{\rm
NG}<1.4$, $-0.3< n_{\rm NG}<1.2$, $-1.1<n_{\rm NG}<0.7$ for the single-field
curvaton, two-field curvaton and DBI scenarios, respectively. We show forecasts
and discuss potential improvements on these bounds, using {\it Planck} and
future CMB surveys.
