  We present a method to sum Borel- and Gevrey-summable asymptotic series by
matching the series to be summed with a linear combination of asymptotic series
of known functions that themselves are scaled versions of a single,
appropriate, but otherwise unrestricted, function $\Phi$. Both the scaling and
linear coefficients are calculated from Pad\'e approximants of a series
transformed from the original series by $\Phi$. We discuss in particular the
case that $\Phi$ is (essentially) a confluent hypergeometric function, which
includes as special cases the standard Borel-Pad\'e and Borel-Leroy-Pad\'e
methods. A particular advantage is the mechanism to build knowledge about the
summed function into the approximants, extending their accuracy and range even
when only a few coefficients are available. Several examples from field theory
and Rayleigh-Schr\"odinger perturbation theory illustrate the method.
