We report the discovery of two new transiting giant exoplanets NGTS-26 b and NGTS-27 b by the Next Generation Transit Survey (NGTS). NGTS-26 b orbits around a G6-type main sequence star every 4.52 days. It has a mass of 0.29^+0.07^-0.06_Mjup and a radius of 1.33^+0.06^-0.05_Rjup making it a Saturn-mass planet with a highly inflated radius. NGTS-27 b orbits around a slightly evolved G3-type star every 3.37 days. It has a mass of 0.59^+0.10^_-0.07_Mjup and a radius of 1.40+/-0.04Rjup, making it a relatively standard hot Jupiter. The transits of these two planetary systems were re-observed and confirmed in photometry by the SAAO 1.0-m telescope, 1.2-m Euler Swiss telescope as well as the TESS spacecraft, and their masses were derived spectroscopically by the CORALIE, FEROS and HARPS spectrographs. Both giant exoplanets are highly irradiated by their host stars and present an anomalously inflated radius, especially NGTS-26 b which is one of the largest objects among peers of similar mass.