Pack waterproof overtrousers if you intend to walk and explore; nothing is worse than soaking wet trousers except....
...soaking wet feet! So you *do* need sensible walking boots/shoes (the ground can be rough) which won't let in the water. Take more pairs of socks than you usually do, just in case your boots leak.
Camping/Beach/Outdoor Gear: Don't underestimate the risks. Whilst Shetland high ground is not especially high, its weather conditions can be as challenging at the Cairngorms, with rabbitholes, rocks and boggy ground ready to break your ankles.
Miscellaneous: If you plan to walk in the wilder parts (such as Northmavine) make sure you have the right emergency gear (food, whistle, spaceblanket, first aid kit, phone..although it may not work) and know how to use a map and compass. I've experienced mist in this area firsthand; without map and compass you will be really stuck. And do make absolutely sure you tell someone where you are planning to walk and when you expect to be back, so they can raise the alarm if you do not return.
Your chances of swift rescue are much, much higher if people actually know you are missing and know where to look for you!
Before you go, buy the Ordnance Survey maps for Shetland: they are truly superb and will give you so much information (including all the archaeological sites which are otherwise not marked). The official site is http://www.ordnancesurvey.co.uk/oswebsite/
Luggage and bags:
If you fly in do check Loganair's cabin baggage limits. Their planes are smaller so their size allowance is smaller too.
Clothing/Shoes/Weather Gear: Absolutely do *not* pack assuming the weather will be good, even if you come in summer. UK weather is changeable and Shetland's weather even more so...and it's very far north. So pack clothes you can layer, adding and taking off as the weather varies during the day.
Pack *good* waterproofs which are windproof as well. Even in summer padded waterproofs are a good idea.
Take hat, scarf and gloves whatever time of year you visit: better to have them than be cold. Hats are anyway essential if you visit the bird colonies by boat (poo on the head!) or walk where bonxies, skuas or fulmars nest (their attacks rarely actually touch you, but they can do so).
And take your sunglasses too......when the sun *does* shine it can be very bright indeed, because the air is so clear and the island so exposed.
Toiletries and Medical Supplies: Mossie spray and antihistamine cream are essential. Shetland doesn't have the midge problem they have in the Highlands (it's too windy) but there are still flying, biting things around
Photo Equipment: Plenty of memory card space and batteries....you'll be taking far, far more photos than you expected to take!
Clothing/Shoes/Weather Gear: A lot of the walks in the area are on marshy ground and there is often quite a biting wind blowing so take a windproof jacket, maybe a beanie to keep your ears warm and good sturdy walking shoes so you don't slip.
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