  Approximation properties of quasi-projection operators $Q_j(f,\varphi,
\widetilde{\varphi})$ are studied. Such an operator is associated with a
function $\varphi$ satisfying the Strang-Fix conditions and a tempered
distribution $\widetilde{\varphi}$ such that compatibility conditions with
$\varphi$ hold. Error estimates in the uniform norm are obtained for a wide
class of quasi-projection operators defined on the space of uniformly
continuous functions and on the anisotropic Besov spaces. Under additional
assumptions on $\varphi$ and $\widetilde{\varphi}$, two-sided estimates in
terms of realizations of the $K$-functional are also obtained.
