We report on the experimental and theoretical investigation of a new class of terahertz filters based on frequency-selective surfaces patterned on thin foils of the low-loss cyclo-olef n polymer Zeonor. We observe both broad and narrowband resonances, which stem from the FSS response and the coupling to substrate guided modes, respectively. The filtering properties are studied as a function of the FSS geometry and the thickness of the polymer layer. Very narrow linewidths with quality factors exceeding 100 are measured experimentally and theoretically confirmed via finite-element simulations.