  It is well-known that every maximal planar graph has a matching of size at
least $\tfrac{n+8}{3}$ if $n\geq 14$. In this paper, we investigate similar
matching-bounds for maximal \emph{1-planar} graphs, i.e., graphs that can be
drawn such that every edge has at most one crossing. In particular we show that
every 3-connected simple-maximal 1-planar graph has a matching of size at least
$\tfrac{2n+6}{5}$; the bound decreases to $\tfrac{3n+14}{10}$ if the graph need
not be 3-connected. We also give (weaker) bounds when the graph comes with a
fixed 1-planar drawing or is not simple. All our bounds are tight in the sense
that some graph that satisfies the restrictions has no bigger matching.
