As always, the conditions required vary by species, but this should provide the basics. Common sense thereafter should be sufficient!

If you have just received your pupae, it is a good idea to lay them on a damp cloth or tissue paper for 10 minutes to rehydrate after travelling. You do not need to do this if you reared them yourself.

A perfect emergence enclosure can be created using polystyrene boxes. This is easy and fairly cheap: a decent sized polystyrene box relative to the number of pupae you are hatching should be easy to buy online. You can then suspend your pupae using pins or glue. Wherever possible, use pins to suspend pupae by their silk pad; if they do not have this intact, a glue gun can be used to secure pupae to a pin or bamboo cane.

Tropical butterflies and moths which enjoy higher humidity and warmer temperatures will benefit from using these boxes as they prevent moisture from escaping and maintain a stable temperature due to the insulating capacity of the box. This is far superior to mesh cages. Native/temperate butterflies are more robust and can typically be kept in a mesh cage without any intervention, although a very fine spray every day or two will benefit the developing butterfly (mimicking the natural hydration gained from rain or dew.) If your home is particularly dry or you use a dehumidifier/air conditioning, I recommend using a polystyrene box as these environmental factors can cause the pupae to dry out and die. Some people opt to use glass enclosures for emergence enclosures, however I find boxes to be far easier to clean and can easily be moved/transported or stored.

A heat mat is often a welcome addition for tropical species, e.g. on the side or base of your emergence enslosure, but never use heat lamps/lights on eggs, caterpillars or cocoons/pupae - this will dehydrate and dessicate them, killing the pupae within a few hours or days. Heat should be moderate and accompanied by high humidity. Room temperature is fine for most silkmoths, hawkmoths, and native or temperate species, however tropical pupae should be kept around 20-24 degrees (set your thermostat to 22 degrees to avoid overheating).

Many of the large silkmoths are very hardy and will emerge fine with normal room conditions, just spray with water once a day. These can be kept in mesh cages so long as you keep up with their need for humidity. Note that if cool for long periods, cocoons may become dormant - this is fine, and they will reawaken when conditions allow. Some Rothschildia species have been known to lie dormant for up to 5 years in wait of ideal conditions. This may be because a given species lives in environments where conditions are only suitable for larvae during optimal periods which do not necessarily occur year-round. This is an excellent survival mechanism for drought- or frost-prone habitats.

Some species also need to go through a period of dormancy before emerging to breed. This is the case for Robin moths and Emperor moths, as they only fly once per year. To break their dormancy, known as diapause, these require cold storage (refrigerator, shed, garage etc; biscuit tin keeps safe from frost and mice). Then incubate for emergence after at least 2-3 months of dormancy.