In this work we introduce, analyze and implement a residual-based a posteriori error estimation for the CutFEM fictitious domain method applied to an elliptic model problem. We consider the problem with smooth (nonpolygonal) boundary and, therefore, the analysis takes into account both the geometry approximation error on the boundary and the numerical approximation error. Theoretically, we can prove that the error estimation is both reliable and efficient. Moreover, the error estimation is robust in the sense that both the reliability and efficiency constants are independent of the arbitrary boundary-mesh intersection.