My suggested exercise sounds pretty similar to Nath's (assuming I've visualized his right).
I hurt my left achilles once in high school, pretty badly. At the time, I was a dumb kid and was pretty insistent on not ever going to the doctor for anything short of steak knife through the hand (actually happened). To this day, I don't know exactly what I did, except that I was literally hopping around on one foot for the better part of a month - it was that long before I could really even put any weight on it at all, and several months before I could really walk with a normal gait, let alone do any kind of strenuous physical activity.
That injury nagged me for years. Every time I got motivated to start running again, I would have to start out the first few times lightly jogging literally a quarter mile - not enough to even get my blood moving - because I knew anything else and it would start giving me trouble and I'd be out of commission for a few weeks again. If I was insanely slow and delicate with it, I could eventually work it up to the point where I could run or do as much as I wanted on it, but the first few weeks/months of any workout regimen required maddeningly slow progress.
In hindsight, I think that the gradual improvement every time I went through an active phase had more to do with the slight/moderate achilles stretch I got from the hamstring stretches I would do before every run, rather than any actual strengthening. I think this because a few years back I finally stumbled on a convenient, more effective achilles stretch (you know: the sort of thing that a doctor or physical therapist could have shown me day one if I'd just gone to the doctor at the time...), and since that discovery, my ankle is an utter non-issue. Since I started doing this stretch regularly (even when not in a workout phase), I haven't felt a peep from that ankle in a couple years now.
Essentially, you just find some place to put your toes, where your heel can hang off the edge (a stair step, a chair, anything), and just crouch forward until your chest is resting on that thigh (you probably won't be able to comfortably support your entire body weight on the one leg from this position at the start, so use your other foot and hands to provide a little balance/support). If your achilles are very inflexible, you'll be astonished at just how intense this stretch is at the start.
As with Nath's, you can work the stretch a little by shifting your weight more towards your knee, or back towards your heel, and leaning side to side a bit.
I think this is probably functionally very similar to Nath's exercise. Just that since you're using your body weight for the resistance, you can drop down and do it pretty much anywhere at a moment's notice (and have a pretty fair bit of weight to work with, even if you're pretty light). The obvious drawback being that you can only do one leg at a time.