Resonances are the cornerstone of photonic applications in many areas of physics and engineering. The spectral position of a photonic resonance is dominated by the structure design. Here, we devise a polarization-independent plasmonic structure comprising nanoantennas with two resonances on an epsilon-near-zero (ENZ) substrate in order to loosen this correlation to obtain less sensitivity to geometrical perturbations of the structure. Compared with the bare glass substrate, the designed plasmonic nanoantennas on an ENZ substrate exhibit a nearly three-fold reduction only in the resonance wavelength shift near the ENZ wavelength as a function of antenna length.