Chill a martini glass while you prepare the cocktail. (see note)
Fill a cocktail shaker with ice. Pour in the pineapple juice, vodka, and lime juice. Cover and shake vigorously until chilled, about 30 seconds.
Strain into the chilled martini glass. Garnish with a pineapple wedge and cherry. Serve immediately.
Notes
You can chill the glass in the freeze ahead of time if you like. Otherwise fill the martini glass with ice and water. Then dump out the ice water before filling. This is a quick chill method that works great.
Bottled lime juice is too tart and will change the taste of the martini. If you don't have limes on hand, you can substitute freshly squeezed lemon juice.
You can add simple syrup to taste if desired to sweeten your drink.