A cylindrical GEM tracker is under construction in order to replace and improve the inner tracking system of the BESIII experiment. Tests with planar chamber prototypes were carried out on the H4 beam line of SPS (CERN) with muons of 150 GeV/c momentum, to evaluate the efficiency and resolution under different working conditions. The obtained efficiency was in the 96 - 98% range. Two complementary algorithms for the position determination were developed: the charge centroid and the micro-TPC methods. With the former, resolutions <100 micron and <200 micron were achieved without and with magnetic field, respectively. The micro-TPC improved these results. By the end of 2016, the first cylindrical prototype was tested on the same beam line. It showed optimal stability under different settings. The comparison of its performance with respect to the planar chambers is ongoing. Here, the results of the planar prototype tests will be addressed.