A detailed investigation of resonance-continuum coupling is carried out both experimentally and theoretically in metamaterials based on high-permittivity dielectric subwavelength resonators. An original experimental scheme is designed at microwave frequencies, which mimics a periodic array of resonators. Fano resonances are discussed in the framework of temporal coupled mode theory for the cases where one or two resonator modes couples to the continuum. Fano lineshapes are unambiguously demonstrated experimentally for the single-mode case in agreement with theoretical modeling. Numerical evidence of resonance trapping is shown in the two-mode case when modes with the same symmetry coincide in frequency.