I had persistent calf pain which started about 6 weeks after a started running and then just got worse and worse. I finally admitted that I had a problem when I couldn't remember the last time I'd been able to go down stairs without using the bannister. I went to a physio and she diagnosed tendonitis (not of the achilles but of one of the tendons on the lower outside of the calf). We eventually fixed it by massage, ultrasound, rest, stretches, strengthening exercises and arch supports.
My advice, for what it's worth, is do no running or other loadbearing exercise for a whole week (swimming is OK) and get a good running shop to check that you've got the right shoe. If all else fails see a physio.
I'm now running harder and longer than I was before but I have no hint of the problem anymore (touch wood).
Millipede