With JMP Pro, you could try bootstrapping:
NamesDefaultToHere(1);
// Sample data
dt = NewTable("Orthogonal Regression",
NewColumn("x1", Formula(RandomUniform(-1, 1))),
NewColumn("x2", Formula(RandomUniform(-1, 1))),
AddRows(50)
);
// Fit orthogonal
fo = dt << Bivariate(Y( :x2 ), X( :x1 ), Fit Orthogonal( Equal Variances ));
// Bootstrap fitted parameters
dt2 = Report(fo)[TableBox(2)] << Bootstrap(1000);
// Look at the result
dt2 << Distribution(
Continuous Distribution( Column( :Intercept ) ),
Continuous Distribution( Column( :Slope ) ),
SendToReport(
Dispatch( {"Intercept"}, "Quantiles", OutlineBox, {Close( 1 )} ),
Dispatch( {"Intercept"}, "Summary Statistics", OutlineBox, {Close( 1 )} ),
Dispatch( {"Slope"}, "Quantiles", OutlineBox, {Close( 1 )} ),
Dispatch( {"Slope"}, "Summary Statistics", OutlineBox, {Close( 1 )} )
)
);