  We present an approximation scheme of the nonperturbative renormalization
group that preserves the momentum dependence of correlation functions. This
approximation scheme can be seen as a simple improvement of the local potential
approximation (LPA) where the derivative terms in the effective action are
promoted to arbitrary momentum-dependent functions. As in the LPA the only
field dependence comes from the effective potential, which allows us to solve
the renormalization-group equations at a relatively modest numerical cost (as
compared, e.g., to the Blaizot--Mend\'ez-Galain--Wschebor approximation
scheme). As an application we consider the two-dimensional quantum O($N$) model
at zero temperature. We discuss not only the two-point correlation function but
also higher-order correlation functions such as the scalar susceptibility
(which allows for an investigation of the "Higgs" amplitude mode) and the
conductivity. In particular we show how, using Pad\'e approximants to perform
the analytic continuation $i\omega_n\to\omega+i0^+$ of imaginary frequency
correlation functions $\chi(i\omega_n)$ computed numerically from the
renormalization-group equations, one can obtain spectral functions in the
real-frequency domain.
