  We present a novel projection-based model reduction framework for parametric
linear time-invariant systems that allows interpolating the transfer function
at a given frequency point along parameter-dependent curves as opposed to the
standard approach where transfer function interpolation is achieved for a
discrete set of parameter and frequency samples. We accomplish this goal by
using parameter-dependent projection spaces. Our main result shows that for
holomorphic system matrices, the corresponding interpolatory projection spaces
are also holomorphic. The coefficients of the power series representation of
the projection spaces can be computed iteratively using standard methods. We
illustrate the analysis on three numerical examples.
