Add white chocolate and shortening to a heat proof bowl. Place the bowl over a medium saucepan with 1 inch of simmering water. Melt the chocolate keeping the water at a simmer, stirring frequently until smooth.
Place pretzels on a wire rack over a parchment lined baking sheet. Pour the white chocolate over the pretzels. Retrieve the excess white chocolate from the baking sheet if necessary. Gently reheat as needed and pour over the remaining pretzels.
Before the white chocolate sets, add one blueberry to each of the small pretzel holes. Place the pretzels in the refrigerator for at least 30 minutes to harden before serving. Store in an airtight container in the refrigerator.