How to choose non-alcoholic beverage pairings for filets mignon?
I have had success pairing steaks with freshly pressed apple juice, as the tartness helps offset the richness and fats of the meat and cheese. An apple/raspberry mix works beautifully, too, as does apple and blackcurrant.

While ginger beer and ginger ale may work, you run the risk of the drink taking over the show, which you don't want.

Two more pairings that work well: Apple and cherry juice is beautiful. Blueberry juice (100% blueberries, with no additives) have much the same mouthfeel as a good red wine, while giving flavor notes all of its own.