Here's a great superset that combines biceps work with a compound movement pattern.
Chin-Up + Smash Curl
By facing the hands back towards you on the pull-ups, more emphasis will be placed on the biceps. We'll also use that same "supinated" position with the biceps curls. We won't actually rotate the hands as they'll stay in the palms facing up and out position.
How to Do It
Starting on the pull-up bar, you'll be using a supinated grip to target the biceps more directly. If you're using a standard straight bar, get your hands in a medium-width grip with your palms facing back towards you. (Many gyms will have transitional handles that place your hands between a supinated and neutral grip, so feel free to use those.) Avoid jumping up to the bar as your shoulder position and swaying momentum will not only take away from your muscle targeting, but potentially put your shoulders in an injurious position. Set up on a box instead.
Pull straight up, peak the contraction for a split second, and then control your range of motion all the way down. Make sure you don't come into a "dead-hang." This will limit the constant tension you're shooting for. Do 4-10 strict reps, tapping into the mind-muscle connection on the biceps.
Now move to the smash curl. Support your chest on an incline bench with your core and glutes engaged. Place your sternum on the top of the bench to allow your arms to move freely.
From here, supinate your hands and drive the middle sides of the dumbbells together as hard as you can, squeezing them with loads of tension. Then curl up, keeping the squeeze on the dumbbells, peak the contraction of the curl, and move back down through a full range of motion.
Do 8-15 reps, really trying to maximize the tension throughout the set. For people who have trouble curling with the volume necessary to achieve a pain-free training effect, this squeeze press is a game changer.