What do you mean by 'quantitate the plasmid after plasmid extraction'? Do you just run the intact plasmid on an agarose gel? If so, you would expect multiple bands for the plasmid, corresponding to various forms of the circular DNA (supercoiled, relaxed, ....). I suggest that you

(1) digest the isolated plasmid with the same enzymes you used to put the insert in and then check the products on an agarose gel. If you have the desired plasmid you should see the vector band and the insert band.

(2) just do sequencing reactions with primers binding ont he vector. If you get the sequence of your insert you can be sure that the insert is in your vector.

I've never seen inserts dropping out of the vector for no reason....

Good luck!

I agree with Michael. You should expect 3 bands for undigested plasmid, corresponded to concatenated (high MW, bright band), relaxed circle (middle band, usually fainter intensity), and supercoiled DNA (lowest MW, also bright, should run about 1/2 to 2/3rd the expected MW for linear plasmid). It is probably a coincidence that your insert and supercoiled DNA have the same size. One other cautionary note- some strains of E. coli already have episomal plasmids, which may be showing up on your gel. Make sure that you are using an appropriate bacterial strain for cloning (such as DH5a).

Completely true answer from Michael and Daniel. You should digest the cloned DNA with unique enzyme and then confirm the actual size, because super coiled DNA are not comparable. Still you find more than one size, possible because of the culture contamination with cells with native plasmid and cloned cells. Do streak the culture on agar plate with antibiotic and do colony PCR from 5 colonies and check weather still there is wild type cells growing. you must gate the cloned vector containing cells as well.