Recently the planar version of the extraordinary magnetoresistance (EMR) magnetic field sensor has been constructed and verified in practice. Planar configuration of the EMR device gives many technological advantages, it is simpler than the classic and allows one to build the sensor using electric materials of the new type (such as graphene or topological insulators) much easier. In this work the planar configuration of the EMR sensor is investigated by performing computational simulations using the finite element method (FEM). The computational comparison of the planar and classic configurations of EMR is presented using three-dimensional models. Various variants of the geometry of EMR sensor components are pondered and compared in the planar and classic version. Size of the metal overlap is considered for sensor optimization as well as various semiconductor-metal contact resistance dependences of the EMR signal. Based on computational simulations, a method for optimal placement of electric terminals in a planar EMR device is proposed.