You could run a real time PCR with probing for at least 2 targets. 1 of them will be probing for the plasmid of your interest; the other(s) should probe a bacterial chromosome gene with only 1 copy to use as DNA standard. By examine the number of plasmids/ number of copies of bacterial gene. One can deduce the number of target plasmid/ host cell.
When you know the size of the plasmid and the yield from a miniprep and also know how dense the culture was, then you can also make an estimation about it.
You could run a real time PCR with probing for at least 2 targets. 1 of them will be probing for the plasmid of your interest; the other(s) should probe a bacterial chromosome gene with only 1 copy to use as DNA standard. By examine the number of plasmids/ number of copies of bacterial gene. One can deduce the number of target plasmid/ host cell.
i am very much in favor of Christians approach, its so easy and old-school. Also, the link given by Abderrahmane Bengrine is useful as the choice of ori has a huge impact on the copy number. Q-PCR based approaches are less accurate and more tedious. Keep it simple!