Well actually a simple google search turned up some answer that might interest you, although I hope you searched yourself before asking?
http://van.physics.illinois.edu/qa/listing.php?id=2635
So basically summing up what the article says, theoretically there are no limits in real life assuming we don't have limited resources and equipment like we have , we could make extremely strong fields , but in the reality with our current capability I would say the upper limit is as the article mentions the one you can achieve with a microsecond explosive type magnetic field.
Look up the EMP , there is a weapon designed specifically to make as strong as possible electromagnetic field for enemy electrical equipment damage also a nuclear detonation makes a very strong magnetic field in a pulsed way.These fields have a high density , yet not even close to the ones on a cosmological scale.
What do you mean by turning solid? Like air or different types of gas, when under high pressure they turn liquid? If so then no I don't think a field of any kind, electric , magnetic can turn into a solid object or even liquid, haven't heard nor seen anything like that happening.