Add the strawberries and water to a small blender or food processor. Puree until smooth. Transfer to a fine mesh colander set over a bowl. Let rest for 5 minutes, then gently stir to separate the puree from some of the seeds. Transfer the puree to a cocktail shaker.

Add the tequila, Cointreau, and lemon juice to the shaker. Add a handful of ice. Shake until chilled, about 20 seconds.

Salt the rim of two serving glasses (about 10 ounces in size) if desired. Fill each glass with ice. Strain the cocktail into each glass. Garnish with strawberries and serve.