  We study the limits to the localizability of events and reference frames in
the $\kappa$-Minkowski quantum spacetime. Our main tool will be a
representation of the $\kappa$-Minkowski commutation relations between
coordinates, and the operator and measurement theory borrowed from ordinary
quantum mechanics. Spacetime coordinates are described by operators on a
Hilbert space, and a complete set of commuting observables cannot contain the
radial coordinate and time at the same time. The transformation between the
complete sets turns out to be the Mellin transform, which allows us to discuss
the localizability properties of states both in space and time. We then discuss
the transformation rules between inertial observers, which are described by the
quantum $\kappa$-Poincar\'e group. These too are subject to limitations in the
localizability of states, which impose further restrictions on the ability of
an observer to localize events defined in a different observer's reference
frame.
