I'm usually a fan of using free weights over machines, but calves are an exception. Machines are simpler and work better. But what if you work out in a home gym or in a bare-bones gym that doesn't have any machines? Then it gets tricky.
The usual staples in this situation are bodyweight single-leg calf raises or standing barbell calf raises. While these are both better than nothing, I'm not a big fan of either.
Single-leg calf raises done with just bodyweight are too easy for most lifters. You can hold a heavy dumbbell in one arm, but even then you're really going to be limited as far as loading potential is concerned. Barbell calf raises offer much great loading potential, but when you do them freestanding, balance becomes the limiting factor.
To circumvent that issue and take the balancing aspect out of the equation, try doing them with the barbell pinned flush against the rack so you're scraping the rack on the way up and down:
For this to work, you need to hold the bar in a front squat position so you can lean into the rack slightly to keep the bar on the correct path.
To increase the range of motion in the stretched position at the bottom of the rep (which is important for growth), stand with your toes on a weight plate or small aerobic step and your heels dangling freely in the air.
You can do them single-leg or double-leg, but I much prefer single leg because a) it just feels better and b) the non-working leg can serve as a "spotter" in case you lose your balance. Balance shouldn't be an issue since you're using the rack for support, but if you do start to feel shaky just tap the free leg down to rebalance yourself. You can also use the free leg for a little added boost at the end of the set to help squeeze out a few more self-assisted "forced" reps.
This is harder than it looks, and when you take into account the friction of the bar against the rack, you probably won't need a lot of weight to really feel it.
To hit the calves in a slightly different way, you can also set up more like a rack pull with a big forward lean, which turns the exercise into something like a donkey calf raise.
These feel quite a bit different from the front squat version, so switch it up and try it both ways.
If you find yourself looking to bring up your calves but train in a machine-free gym, these may be just what the doctor ordered.