Coulomb excitation is one of the rare methods available to obtain information on static electromagnetic moments of short-lived excited nuclear states, including collective non-yrast levels. It is thus an ideal tool to study shape coexistence and shape evolution throughout the nuclear chart. Historically, these experiments were limited to stable isotopes, however the advent of new facilities, providing intense beams of short-lived radioactive species, has opened the possibility to apply this powerful technique to a much wider range of nuclei. Here, we present some recent complex Coulomb-excitation studies and use the example of superdeformed states in 42Ca to demonstrate the sensitivity of the method to second-order effects such as relative signs of electromagnetic matrix elements and quadrupole moments.