If using apples as “cups” to serve, cut tops off of apples. Using melon baller, scoop out inside of each apple to form a cup, being sure not to make a hole into the bottom of the cup. Use pastry brush to brush lemon juice on cut parts of each apple.

Place caramel sauce on small plate. Place sugar and cinnamon on second small plate; stir to combine.

Dip the rim of each apple cup (or glass, if using) in caramel sauce, allowing excess sauce to drip off before dipping into sugar mixture. Place cups upright on serving platter.

In pitcher, stir sparkling cider, cider and rum until well combined. Divide cider mixture between apple cups or glasses. If serving in glasses, garnish each glass with an apple slice. If serving in apple cups, not all cider mixture will fit in cups. Set pitcher with remaining cider mixture out so guests can refill their apple cups as needed.