  Let $\Omega$ be a domain in $\mathbb{R}^n$, $\Gamma$ be a hyperplane
intersecting $\Omega$, $\varepsilon>0$ be a small parameter, and
$D_{k,\varepsilon}$, $k=1,2,3\dots$ be a family of small "holes" in
$\Gamma\cap\Omega$; when $\varepsilon \to 0$, the number of holes tends to
infinity, while their diameters tends to zero. Let $\mathscr{A}_\varepsilon$ be
the Neumann Laplacian in the perforated domain
$\Omega_\varepsilon=\Omega\setminus\Gamma_\varepsilon$, where
$\Gamma_\varepsilon=\Gamma\setminus (\cup_k D_{k,\varepsilon})$ ("sieve"). It
is well-known that if the sizes of holes are carefully chosen,
$\mathscr{A}_\varepsilon$ converges in the strong resolvent sense to the
Laplacian on $\Omega\setminus\Gamma$ subject to the so-called
$\delta'$-conditions on $\Gamma$. In the current work we improve this result:
under rather general assumptions on the shapes and locations of the holes we
derive estimates on the rate of convergence in terms of $L^2\to L^2$ and
$L^2\to H^1$ operator norms; in the latter case a special corrector is
required.
