Well actually a simple google search turned up some answer that might interest you, although I hope you searched yourself before asking?
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.