Shock-droplet interactions occur in a spectrum of high-speed propulsion systems e.g. scramjets and rotating detonation engines. When the combustion chamber pressure nears the critical pressure of the fuel/air mixture, transcritical behavior involving the transition from liquid-like to gas-like states is expected. We consider the interaction of a shockwave with a liquid droplet at near-critical conditions. A multiphase diffuse-interface solver coupled with the Peng-Robinson equation of state is developed to accurately determine the state of the fluid as the shock propagates through the droplet. The results show the influence of varying the initial temperature of the droplet and the shockwave strength on the droplet instabilities and breakup behavior.