Opposing Muscle Groups

It's a common practice to work out opposing muscle groups during the same workout:

biceps + triceps,
quadriceps + hamstrings,
chest + back,
extensors + flexors (top and bottom) of forearms
hip abductors + hip adductors...

Supersetting these groups is effective: do a set for one muscle then without rest do a set of the other. Training chest + back, or biceps + triceps, like this makes the arms, the entire upper body, feel very pumped and large.

Both of the muscles that oppose each other must be trained paying equal attention to each one--if not on the same day, then on separate days of the week.

The size of one muscle is ultimately limited by the size of the muscle that opposes it. The biceps can only get so big if the triceps aren't trained at all, or with the same attention and intensity. The chest is limited by the size of the back, and so on.

So then what is the opposing muscle group to the calves (gastrocnemius and soleus)?

The calves do have an opposing muscle group--the tibialis anterior, that runs vertically along the tibia, the shin.

Few people specifically train their tibialis anterior.
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Big calves are a rarity.

After I train my calves, I do tibialis raises while seated with "light" dumbbells on my feet. Sit up straight, with good posture, like there is an imaginary thread pulling your body upward, exiting out the top of your head. Start light, but move up. It may feel awkward at first to balance the weights on your feet. You'll notice that hardly anyone takes the time to do this. It is worth it. I can make this exercise hurt intensely because these muscles burn like no other muscles on my body. But it hurts so good. :)

Here are more exercises for the tibialis anterior (they don't have a seated version with weights, though).