  The NA48/2 and NA62-$R_K$ experiments at CERN collected large samples of
charged kaon decays in 2003--2004 and 2007, respectively. These samples,
collected with different trigger conditions, allow to search for both short and
long-living heavy neutrinos produced in $K^{\pm}\to\mu^{\pm}N_4$ decays. The
results of these complementary searches are presented in this letter. In the
absence of observed signal, the limits obtained on
$\mathcal{B}(K^{\pm}\to\pi^{\mp}\mu^{\pm}\mu^{\pm})$, $\mathcal{B}(K^{\pm}\to
\mu^{\pm} N_4)\mathcal{B}(N_4\to \pi\mu)$, $\mathcal{B}(K^{+}\to\mu^{+}N_4)$
and on the mixing matrix element $|U_{\mu4}|^2$ are reported.
