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We simulate electromagnetic (EM) measurements acquired with a logging‐while‐drilling (LWD) instrument in a borehole environment. The measurements are used to assess electrical properties of rock formations. Logging instruments as well as rock formation properties are assumed to exhibit axial symmetry around the axis of a vertical borehole. The simulations are performed with a self‐adaptive goal‐oriented ‐finite element method that delivers exponential convergence rates in terms of the quantity of interest (for example, the difference in the electrical current measured at two receiver antennas) against the CPU time. Goal‐oriented adaptivity allows for accurate approximations of the quantity of interest without the need to obtain an accurate solution in the entire computational domain. In particular, goal‐oriented ‐adaptivity becomes essential to simulating LWD instruments, since it reduces the computational …