The SSE is the residual sum of squares of the best fit of the current model to the data. The Goal SSE for confidence limits is only used for estimating the confidence limits at current Alpha (there is a description in the JMP documentation in the "statistical details" of the nonliear chapter).
Although R2 alone should not be used to judge if a nonlinear model's fit is "good", it can be calculated from the SSE and raw data.
Try this JSL example (I only tested it in JMP 10, I don't remember if the the sample table came with JMP 8. If the path fails, try to open the table manually before running the remainder of the script)
// Example nonlinear fit
dt = Open( "$SAMPLE_DATA/Nonlinear Examples/US Population.jmp" );
nlin = dt << Nonlinear( Y( :pop ), X( :Name( "X-formula" ) ), Finish() );
// get SSE from report
SSE = Report( nlin )[Number Col Box( "SSE" )][1];
// Calculate total sum of squares (i.e. of distances from y mean)
SStot = Sum( ((Column( 2 ) << get as matrix) - Col Mean( Column( 2 ) )) ^ 2 );
// Calculate R2 and adjusted R2
R2 = 1 - SSE / SStot;
R2adj = 1 - (SSE / Report( nlin )[Number Col Box( "DFE" )][1]) / (SStot / Col Number( Column( 2 ) ) - 1);
// Update report with R2
Report( nlin )[Outline Box( "Solution" )] << prepend(
H List Box( Number Col Box( "R2", {R2} ), Number Col Box( "R2adj", {R2adj} ) )
);