Numerical simulations of the use of ultra-short-pulse reflectometry to diagnose plasma density and magnetic-field profiles are presented. Numerical solutions of Maxwell's equations are used to model the propagation of ordinary modes into a plasma from whose reflected signals' time-of-flight (group delay) as a function of frequency is deduced the electron density profile. Similar methods are used to simulate the propagation and reflection of extraordinary waves, from which is deduced the magnetic-field profile if the electron density is already known (the cutoff relation for the extraordinary mode depends jointly on the electron density and the magnetic field). The simulation results presented here demonstrate that the determination of plasma density and magnetic-field profiles from ultra-short-pulse reflectometry is relatively robust. In order to use more realistic plasma and magnetic-field configurations in the reflectometry simulations as well as to be able to simulate, assess, and tune the performance of the diagnostic in the experimental configurations of interest, O-mode and X-mode reflectometry simulation packages have been merged into the CORSICA comprehensive plasma modelling framework. Examples of CORSICA reflectometry simulations of the DIII-D tokamak and the SSPX spheromak being built at the Lawrence Livermore National Laboratory are presented.