  In this work we explore and test new formulations of cosmological scenarios
in $f(Q)$ theories. In these settings, the non-metricity scalar ($Q$) is the
main source of gravity and Friedmann equations are modified to account for the
associated degrees of freedom. This work focuses first on the derivation, and
then theoretical and observational analysis of two such (new) exact
cosmological models; they both display a non-standard behaviour in which an
additional parameter encoding non-metricity effects acts in the fashion of a
screened cosmological constant. One of the new settings has the same background
evolution as the well know DGP cosmological model, while the other resembles
the former considerably, although its origin is purely phenomenological. We use
the Markov Chain Montecarlo method combined with standard statistical
techniques to perform observational astrophysical tests relying upon background
data, specifically these are Type Ia Supernovae luminosities and direct Hubble
data (from cosmic clocks), along with Cosmic Microwave Background shift and
Baryon Acoustic Oscillations data. In addition, we compute some of the
cosmographic parameters and other discriminators with the purpose of refining
our knowledge about these models in the light of their theoretical and
observational signatures, and this allows for a better comparison with the
(concordance) $\Lambda$CDM setup. We conclude that these scenarios do not show
signatures indicating a departure from the $\Lambda$CDM behaviour.
