Had a similar problem a few years back. I found that it is highly dependent on the shoes you wear? Do they press or pinch around your ankle at all?
Stretching your calf is excellent advice...
This excersize is similar to that described by UnaDogger, but allows stretching of both calf muscles. I would do this by placing the front of my foot on something like a brick or raise it up against a wall or tree as much as possible with the heel on the ground. (rocks with 45-55 degree inclines are really good) Keep your feet shoulder width apart, the leg you are strecthign should be approximately 1 step forward and legs straight before and during the stretch. Move your hips forward over the leg you are stretching. You can also stretch the outside calf muscle in an almost identical excersize. This time bending the knee of the leg you are stretching somewhat. Again, move your hips forward and as you do this slightly angle your knee toward the inside, you will feel it in the outer part of the calf.
If either muscle is tight it might affect your achilles. Stretch both... and everything else while your at it.
Again, check your boots. I got it from old boots that lost support around my ankle from bending side to side and it started pinching my achilles without me noticing right away.
Calf raises should help. Icing and NSAIDS only seem to abate the pain indicating the presence of inflammation, IMO try to stretch and gradually strengthen the muscle. Tendonitis commonly develops from injured/strained muscles/tendons that become somewhat weak.
Being a climber, I have had a lot of tendonitis and tendon injuries. As a result I have found warm-ups are essential and that stretching is an absolute must and something that I will make myself do everyday and multiple times during an activity, and MOST IMPORTANTLY AFTERWARDS.
Best of luck to you.
Justin
Edit: Ice & NSAIDS are typically useful immediately after an injury to help the healing process. I say to stay away from them while hiking, because I feel they blind you to overuse of the particular muscle/tendon. If you gradually strengthen and stretch the muscle they should not be necessary. If they are necessary it seems that the tendon needs more of a recovery time. If you do hike to the point where you need to ice it, this will be a cycle that continues... strengthen and stretch before a hike... overdo it on the hike injure the muscle ... nsaids and ice, then stretch and strenthin again.. . then overdo it on the hike... and so on. Be Careful & good luck.