Using the transverse field muon spin relaxation technique, we measure the temperature dependence of the magnetic field penetration depth lambda, in the NaxCoO2.yH(2)O system. We find that lambda, which is determined by the superfluid density n(s) and the effective mass m*, is very small and on the edge of the TF-microSR sensitivity. Nevertheless, the results indicate that this system obeys the Uemura relation. By comparing lambda with the normal state electron density, we conclude that m* of the superconductivity carrier is 70 times larger than the mass of bare electrons. Finally, the order parameter in this system cannot be described by a complete gap over the entire Fermi surface.