We report on our study of high-energy properties of two peculiar TeV emitters : the “ extreme blazar ” 1ES 0347 - 121 and the “ extreme blazar candidate ” HESS J1943+213 located near the Galactic Plane . Both objects are characterized by quiescent synchrotron emission with flat spectra extending up to the hard X-ray range , and both were reported to be missing GeV counterparts in the Fermi -LAT 2–year Source Catalog . We analyze a 4.5 year accumulation of the Fermi -LAT data , resulting in the detection of 1ES 0347 - 121 in the GeV band , as well as in improved upper limits for HESS J1943+213 . We also present the analysis results of newly acquired Suzaku data for HESS J1943+213 . The X-ray spectrum is well represented by a single power law extending up to 25 keV with photon index 2.00 \pm 0.02 and a moderate absorption in excess of the Galactic value , in agreement with previous X-ray observations . No short-term X-ray variability was found over the 80 ks duration of the Suzaku exposure . Under the blazar hypothesis , we modeled the spectral energy distributions of 1ES 0347 - 121 and HESS J1943+213 , and derived constraints on the intergalactic magnetic field strength and source energetics . We conclude that although the classification of HESS J1943+213 has not yet been determined , the blazar hypothesis remains the most plausible option , since in particular the broad-band spectra of the two analyzed sources along with the source model parameters closely resemble each other , and the newly available WISE and UKIDSS data for HESS J1943+213 are consistent with the presence of an elliptical host at the distance of approximately \sim 600 Mpc .