The issues of variability and uncertainty of tidal speed result in severe challenges for standalone microgrid (as island grids for examples) operators. Indeed, to maintain the system power balance, existing classical generators which are associated with tidal power units must be able to frequently change their operating point, either up or down, to respond to the fast fluctuations of tidal power and consumption and sometimes exceed their maximal ramp capability. This in turn accelerates aging process and results in serious damage. The switching to a safer and more reliable system seems to be a promising and long-term solution. This paper proposes to associate a supercapacitor-based Energy Storage System (SC-ESS) to a tidal turbine to smooth the fast power production fluctuations. The association of this SC-ESS with the tidal turbine unit aims to meet requirements on the variation of injected tidal power in an islanded microgrid. An original smart power management strategy is proposed for the use of the ESS. Taking into account this strategy, an optimal design methodology based on simulations on the more severe encountered day cases is proposed. This methodology allows to determine a minimal sizing of the ESS to fulfil the grid requirements. The paper also proposes a complete modeling of the whole system behavior. The Energetic Macroscopic Representation (EMR) tool is used to realize the system model where the inversion-based control principle is then used to deduce the control schemes. This global methodology is applied to a test tidal turbine which is based on a real 1 MW prototype setup to the islanded grid of Ushant in France. Using real measured data, it is shown that a relatively small and low cost SCs pack is sufficient to accommodate the high tidal power fluctuations. A comparison is performed between the existing configuration where a resistor bank is used to shave the excessive power variation and the considered case where SCs pack is used. For one tidal cycle, it is shown that a reduction in energy loss of 18.2% is achieved, which presents a non-negligible gain for Ushant's Island microgrid.