The concept of a "warrant" is for A to give B permission to invade C's property. This of course is incompatible with any concept of freedom; it makes no more sense than A giving B permission to rob C, or kill him. It is entirely a statist concept.
But, regarding searching property that you don't have permission to be on, there are basically two possibilities:
Pre-consent: part of your agreement with your private defense agency is to allow their representatives to search your property if they have sufficient evidence. Unlike the cops, they are liable for any damage they do, and if they abuse the contracted privilege then you can switch to another company. The incentive for individuals to allow this sort of contract is that it will engender trust with others—if someone does not allow a defense company with a history of good behavior to have this contracted search right, others may not wish to do business with them. (On the other hand, they may not care. People can make their own choices.)
- Invade anyway, and accept the consequences: break in because you believe you can find evidence of a crime (harm). If you find it, you're fine; if you don't, you get to pay damages (probably a lot of damages).
A warrant in a statist society does not, after all, convey any new right; it just asserts that the police invaders' masters have given their permission—a permission they have no right to give. And so, with this illegitimate permission, they (by force, not right) invade the property of the owner. I.e., even today, police exercising a warrant are committing a crime against the property owner. It's not different in a free society, except that it is better understood that Magic Paper doesn't exist.
However, a free society necessarily denies the existence of a magic right to invade someone else's property because you want to, or because some self-created authority says so. (DBR)