Drain cherries thoroughly and place on paper towels to dry completely, at least 30 minutes. Any moisture will prevent the chocolate from sticking properly.
In a medium bowl, beat together butter and corn syrup until smooth. Gradually add powdered sugar, almond extract, and salt, mixing until a stiff dough forms.
Take about 1 teaspoon of fondant mixture and flatten it in your palm. Wrap it around a cherry, leaving the stem exposed. Roll gently to smooth. Place on a parchment-lined baking sheet.
Repeat with remaining cherries and refrigerate for at least 1 hour until firm.
In a microwave-safe bowl, combine chocolate chips and shortening. Microwave in 30-second intervals, stirring between each, until completely smooth.
Holding each cherry by the stem, dip into melted chocolate, swirling to coat completely. Let excess drip off, then place on parchment paper.
Refrigerate cordials for at least 1 hour to set. Store in an airtight container in the refrigerator for up to 2 weeks. The fondant will soften and become creamy after a few days—that's the magic!