Lyα emitter (LAE) surveys have successfully used the excess in a narrowband filter compared to a nearby broadband image to find candidates. However, the odd spectral energy distribution (SED) of LAEs combined with the instrumental profile has important effects on the properties of the candidate samples extracted from these surveys. We investigate the effect of the bandpass width and the transmission profile of the narrowband filters used for extracting LAE candidates at redshifts z ~= 6.5 through Monte Carlo simulations, and we present pilot observations to test the performance of tunable filters to find LAEs and other emission-line candidates. We compare the samples obtained using a narrow ideal rectangular filter, the Subaru NB921 narrowband filter, and sweeping across a wavelength range using the ultra-narrow-band tunable filters of the instrument OSIRIS, installed at the 10.4 m Gran Telescopio Canarias. We use this instrument for extracting LAE candidates from a small set of real observations. Broadband data from the Subaru, Hubble Space Telescope, and Spitzer databases were used for fitting SEDs to calculate photometric redshifts and to identify interlopers. Narrowband surveys are very efficient in finding LAEs in large sky areas, but the samples obtained are not evenly distributed in redshift along the filter bandpass, and the number of LAEs with equivalent widths <60 Å can be underestimated. These biased results do not appear in samples obtained using ultra-narrow-band tunable filters. However, the field size of tunable filters is restricted because of the variation of the effective wavelength across the image. Thus, narrowband and ultra-narrow-band surveys are complementary strategies to investigate high-redshift LAEs.