I don't have a scale (but I'm thinking of getting one so I'm glad you posted this question). But determining how much yarn is in an ounce/lb. is a two-fold
You will want a scale and something called a McMorran balance. Here is more info I found for you from a Google search, there may be better descriptions out there: link
You determine the "balance" size of a pice of yarn. Then you measure it against a ruler and use an equation to determine # of yards per ounce or per pound (depending on equation used). Then when you weigh a skein you can determine how many ounces/pounds you have left and therefore how many yards that is.
It might sound scary or hard but it's actually really easy.
My Mom was stashbusting (some was from 1970-something Convergence!) and I mailed an obscene amount of stuff home. Hardly any of it was labelled though so I got a crash course in burn tests and weighing and measuring (McMorran balance and small postal scale that you can buy at the drug or grocery store - but I'm not sure how sturdy those are and if they stay accurate over time). It kept me busy for a day and a half.
ETA: Of course, if you still have the skein label... maybe it's as simple as determining how many yards per ounce the whole skein had and then weigh the left over applying the same ratio?