I love horseradish so I serve the rum-sauced tenderloin with horseradish mashed potatoes... But I think a nice mild horseradish sauce would be yummy on a tenderloin.
I say "mild" because I've noticed that a lot of horseradish sauces tend to be quite pungent and overwhelming for the mild flavor of a tenderloin. A stronger sauce would be more suited to a more flavorful, fattier cut- maybe prime rib?