Calf Raises - Calf raises are one of the easiest weightless calf exercises. You can do this exercise just about anywhere. Make sure that you are on a flat surface, such as a hardwood floor. Start out by keeping good posture, standing as straight up as possible, with your head forward. Lift your toes slightly off the ground (not much at all) to move most of your body weight toward your heels. From this position, shift all of the weight over to your toes, and go up into a tip-toe position, like a ballerina. Lower yourself back down and repeat. Start out by doing 4 sets of 20 calf raises.
Exploding Calf Raises - Exploding calf raises have the exact same concept of calf raises with one difference. Instead of stopping your motion at the toes, you are going to push yourself off the ground. Start by doing a normal calf raise. When you reach the peak position (where you are on your tip-toes) use the momentum that you have build up to jump slightly off the ground. You should still be keeping the same form as a normal calf raise, and you should barely be leaving the ground. This exercise is good for your calves but also build explosive power, similar to plyometric exercises. Start out by doing 3 sets of 15 exploding calf raises.
Stair raises - In a gym, you would normally use a platform weight machine to do stair raises. However, a basic set of stairs will work just fine. Start by standing on a stair, with your front facing the top of the steps. Back up slightly so that your heels are off of the step and your toes are still on the step. Release tension in your calves and ankles so that your body lowers slightly. This will drop your heels into a slightly lower position. From this position, go up into a tip-toe position so that you are on the balls of your feet. Go back down to starting position, and repeat. This exercise is great for the calf muscles as it uses gravity as resistance. Start out by doing 4 sets of 15 stair raises. Make use of the first step at the base of the steps to do stair raises. No reason to go tumbling backwards if something were to happen.
Jumping Rope - Jumping rope is one of the best calf exercises available, with or without weights. Not only does jumping rope increase calf strength, but it also adds aerobic exercise to your workout as well. To focus on calve muscles, make sure that you are always staying on your toes when jumping rope.
Be sure to only work out your calf muscles once a week. You already use your calf muscles quite a bit just by everyday walking. Give them some time to heal after a workout. These exercises are actually very effective considering that they do not use any weights as resistance. If you are breezing through your weightless-calf workout with ease, try adding on 10 more reps to each exercise. This should make your workouts more challenging.