I know it's hard a question to answer but a ball park figure.
The only way you will get a precise answer is by getting 3-4 estimates from local contractors.
I've seen costs of screened porches from $20 to $80 /sf. Since most of them are custom built, involving multiple trades, to your specs, lot, house and taste, the price per sf varies a lot. In some cases even tops $100/sf.
i'm a boston contractor. like dj said, it's a hard thing to estimate based on many many factors. foundation or piers? PT or composite? removable screens, permanent screens, screens starting above a knee wall? flat roof, angled room? interior of roof bare, beadboard, drywall? the list goes on and on. something very very cheap could run about $35+ per sq ft and there really isn't a limit as to how much you could spend.