Hibernation (brumation) is generally considered beneficial for tortoises that would naturally hibernate in the wild.  Make certain of this, Testudo graeca from some locals, for instance, do not hibernate.

A tortoise that is underweight or not 100% healthy should never be hibernated. If you are not confident of judging this yourself, then a skilled reptile veterinarian should give your tortoises a thorough check-up.

Before hibernation, a tortoise should be gradually cooled and feeding should be stopped. It is important that a tortoise doesn't enter hibernation with food still in its stomach, so as the time for hibernation approaches, the desire to feed will be gradually reducing due to the drop in temperatures.

Once feeding stops, the tortoise should be bathed regularly to encourage it to pass anything left in its digestive system. A fasting period of one month, immediately prior to hibernation, at cool temperatures (but not cold enough to cause the tortoise to begin hibernating!) is recommended. During this time it should be encouraged to drink, since it is important that the tortoise does not go into hibernation without drinking beforehand, in order to prevent dehydration.

A particularly safe method of hibernation is using a reliable (i.e. Not a second-hand cast-off!!!) clean, domestic fridge. You can break the air tight seal with a small rod, taped to the fridge, so that it keeps the rubber gasket on the door from sealing completely. Too much of a gap and you'll have trouble with the temperatures if there is a warm spell.

The ideal temperature should be kept around 4°C - 5°C (39°F - 41°F) and a Max/Min (Hi/Low) thermometer (preferably with alarm functionality) used to monitor the temps. The Minimum monitored temperature should not drop below 2°C (36°F) and the maximum should not exceed 8°C (46/47°F). Bowls of clean water can be kept in the fridge at the same time, to increase thermal stability.

The tortoises are put in open cardboard boxes with shredded newspaper. The fridge should be in a cool room (such as a garage), and the tortoises checked when temperatures are low, to minimize the rise in temperature inside the fridge when the door is opened. However, since the inside of the fridge can only be at the same temperature, or cooler, than the surrounding air, there should be provisions made to ensure that the chosen location doesn't drop below the critical minimum temperature.

The tortoises should be checked daily and if they have urinated, then they are in danger of dehydration and they should be woken up, given plenty of water and kept in a warm, bright vivarium for the remainder of the winter. They should also be weighed regularly and if they are losing significantly more than 1% of their original weight, per month, then they should be woken.

Hibernations do not need to be as long as most people believe and in fact they put the tortoises in unnecessary danger of increased post hibernation problems. An ideal period is around 3 months, since this approximates the natural hibernation period of most Mediterranean tortoises in the wild, but this will obviously result in heated, bright, indoor accommodation being necessary for much of the late autumn and/or spring.  Again, make certain your species would naturally hibernate before attempting this.

After the hibernation is complete, the priority is to warm the tortoise up, using controlled overhead heating, and as soon as that is achieved, to get it drinking. (Feeding is definitely of secondary importance to getting the tortoise to drink.) Drinking is most likely to be encouraged if the tortoise is stood in a shallow dish (or sink) of warm water. If you have trouble getting your tortoise to drink immediately on waking from hibernation (or to feed, within 1 week) then you should contact a tortoise specialist veterinarian for further advice and possible treatment.

Mail to the author - Alex. Dempsey

References:
(1) "Safer Hibernation & Your Tortoise" by Andy C Highfield.
(Tortoise Trust Care sheet).