  We compute the electromagnetic charged kaon form factor in the time-like
region by employing a Poincar\'e covariant formalism of the Bethe-Salpeter
equation to study quark-antiquark bound states in conjunction with the
Schwinger-Dyson equation for the quark propagator. Following a recent kindred
calculation of the time-like electromagnetic pion form factor, we include the
most relevant intermediate composite particles permitted by their quantum
numbers in the interaction kernel to allow for a decay mechanism for the
resonances involved. This term augments the usual gluon mediated interaction
between quarks. For a sufficiently low energy time-like probing photon, the
electromagnetic form factor is saturated by the $\rho(770)$ and $\phi(1020)$
resonances. We assume $SU(2)$ isospin symmetry throughout. Our results for the
absolute value squared of the electromagnetic form factor agree qualitatively
rather well and quantitatively moderately so with available experimental data.
