A sufficiently large radio system built on Mars or at its solar LaGrange point could provide the shielding effect that is normally the responsibility of the magnetosphere. It was studied for feasibility by NASA and found possible with current technology. Of course, possible doesn't imply practical and the natural formation of Martian atmosphere if we did that would be on geologic timescales.
Water would get blown away over a period of millions of years though. I think that's not much of a problem.
Even if you could increase the atmospheric density, the lack of magnetosphere is still a problem when it comes to human habitation, however. Any long-term habitats would need to be built underground, or at least heavily shielded against solar radiation.
Could people go out at night?
I've previously seem ideas such as nuking the poles. It implied there were enough gases stored in the ice to created a sufficient atmosphere. The loss of the atmosphere due to lack of a magnetosphere would take millions of years.