A rotational rheometer can be used as an interfacial shear rheometer (ISR) by means of proper accessories that allow one to shear fluid-fluid interfaces in a controlled manner. One of the most used accessories, even commercially available, is based on a biconical bob geometry. However, recovering the correct values of the rheological variables is far from trivial. A strategy that has proved to be successful in other ISRs is to properly account for the interface and subphase drags by numerically finding the corresponding flow fields and, then, use an iterative scheme to recover the proper values of the complex Boussinesq number and, consequently, the dynamic surface moduli. Here, we propose to use such a scheme for the biconical bob oscillatory rheometer. We compare our solution with different well known previous approximations, and discuss under which conditions those approximations may lead to errors in the data processing. We have tested the performance of our design and numerical framework on several interfacial systems, comparing the results to those obtained through a magnetic needle rheometer (ISR). We demonstrate that, even for relatively low values of the Boussinesq number, the numerical flow field solution here proposed allows one to precisely reproduce the results obtained by the ISR, while those approximations based on a linear velocity decay at the interface may introduce spurious effects on the calculation of the dynamic surface moduli. (C) 2017 The Society of Rheology.