Granty,
You can run through mild shin splints - I seem to recall you said you were suffering from tight calves and there is often a connection.
Shin splints covers a variety of conditions such as medial tibial stress syndrome (MTSS), stress fractures and compartment syndrome. The latter two are characterised by a crescendo pain i.e. the pain comes on after running for a while and gradually gets worse. MTSS there is usually some discomfort to start with but once the musles have warmed up the pain eases even disappears but may come back later after you've stopped running.
You need to try and keep your stride short, make sure your feet land under your centre of balance, ice your shins after every run for about 15 mins (this will help to reduce the swelling) and there are some strengthening exercises you can do to protect your shins (have a look at
http://www.brooksrunning.co.uk/uk_shin-splints.html).
I suffered quite badly with very sore and swollen shins a few weeks ago. My podiatrist thought it was tibial peristisis, which is an inflamation of the tissues around the shin bones and is almost always linked to overpronation (there is also a higher risk of stress fractures). The pod thought this because the pain and swelling was along the front of the shin about a third up an and not on the inside down towards the ankle as it is with classical MTSS. He wanted me to take complete rest for about a month but I was in the middle of training for the Plymouth Half so as a compromise I had to reduce my training intensity by 25% and wear shin supports. I had to slow down my running pace so I trained with a slower runner at club and I substitued one of my sessions for a treadmill. My orthotics were also adjusted.
My shins have improved but I still can't train on consequtive days without the discomfort starting to return, which is a little frustrating as I want to follow an improvers half marathon plan which is 4 days a week. I'm still trying different shoe/orthotic combinations to find the most comfortable solution.
Granty if your shins don't start to improve I would consider seeing a physio or podiatrist just to get your biomechanics sorted out - make you don't have an unusual gait. How old are your shoes? How much mileage have they done?
Best of luck and try not to overdo it.