  We demonstrate that future radius measurement of the NICER mission have the
potential to reveal the existence of a strong phase transition in dense neutron
star matter by confirming the existence of so called twin stars, compact star
configurations with the same mass but different radii. The latest radius
constraints from NICER for the pulsars J0740+6620 as well as J0030+0451 are
discussed using relativistic mean field equations of state with varying
stiffness, connected with a first order phase transition to quark matter. We
show, that twin star solutions are compatible with the new radius constraint
but are located at radii \emph{below} the present constraints from NICER
serving as a smoking gun for a strong phase transition in neutron star matter.
This scenario is realized if a strong phase transition takes place in neutron
stars of the first branch with masses above $2\,M_\odot$.
