The frequency dependence of seismic properties of fully saturated rocks can be related to wave-induced fluid flows at different scales. The elastic dispersion and attenuation of four fluid-saturated carbonate rocks, with different microstructures, have been measured over a broad frequency range in the laboratory. The selected rocks were a presalt coquina from offshore Congo, an Urgonian limestone from Provence (France), and an Indiana limestone either intact or thermally cracked. The selected samples present a variety of pore types characteristic of carbonates, and their link with potential squirt flow dispersion was investigated. To cover a broad frequency range, forced oscillations (0.004 to 100 Hz) and ultrasonic (1 MHz) measurement techniques were performed in a triaxial cell, at various differential pressures, on the samples saturated by fluids of different viscosity. Both hydrostatic and axial oscillations were applied in order to get the different dynamic moduli. For all our samples, the drained/undrained transition and the squirt flow mechanisms were characterized experimentally, in terms of amplitude of dispersion, amount of viscoelastic attenuation, and frequency ranges. Biot-Gassmann's theory was found to apply mainly at seismic frequencies (10-100 Hz). A potential correlation between pore type and possible squirt flow dispersion was investigated. Intragranular microporosity, with either a rimmed or uniform distribution, does not seem to generate any substantial dispersion. On the other hand, cracked intergranular cement and uncemented grain contacts seem to generate substantial squirt flow dispersion, at respectively seismic and sonic log frequencies.