There should be an add-in which allows generating regression lines accounting for errors in both X and Y. Usually york fit is used for this purpose in other software. It is crucial that JMP also introduces this feature.
In the Bivariate platform, use the Fit Passing Bablok option to fit a regression model using the Passing-Bablok method. Passing-Bablok regression was developed for comparing measurements from two different analytical methods. The method assumes a linear relationship between the two variables with strong correlation. A line of fit and a dotted line for Y = X are added to the scatterplot. Use the Bland Altman Analysis option in the Passing-Bablok Fit red triangle menu to perform a paired t-test and Bland-Altman analysis.
If you can specify the variance ratio between both errors, you can use Deming fit, which is available via:
The actual issue in JMP: the best regression options are hidden in the bivariate Report - and not available via Graph Builder !??! here is a wish to fix the issue: Graph Builder: robust regressions
As mentioned in a previous comment, you can perform a Deming regression in JMP under the "Fit Orthogonal" menu and specify the error ratio between X and Y. This assumes a constant measurement error ratio between the variables and expects that errors are normally distributed and independent. The Passing-Bablok might be the better choice which has less requirements for the error distributions of X and Y. As mentioned in a previous comment, this regression option is now available.
The York regression is an interesting suggestion. We will consider the expanded use-cases of this vs. the Deming and Passing-Bablok options currently available. Thank you for posting.