Great post Rick!
I'm trying to do a simple profile marginal likelihood, for the parameters of the covariance with nlmixed.
It's very easy to get the output in glimmix and mixed with COVTEST (to obtain statistical inferences for the covariance parameters).
Specifically, I'm trying to get the loglikelihood to be able to plot the marginal profile likelihood of the covariance parameter elements.
It seems in the manual of NLMIXED that CovMatParmEst, is the way to go, but I cannot get an evaluation of the probability of each parameter value in the grid.

Using your example :

ods output ParameterEstimates=pe
ConvergenceStatus=p2
CovMatAddEstCorrMatAddEst=p3
CorrMatParmEst=p4
CovMatAddEst=p5
CovMatParmEst=p6;

proc nlmixed data=pump ECORR CORR ECOV COV EDER;
parms logsig=0 to 1 by .1; /* read guesses for parameters from data set */

if (group = 1) then
eta = alpha1 + beta1*logtstd + e;
else eta = alpha2 + beta2*logtstd + e;
lambda = exp(eta);
model y ~ poisson(lambda);
random e ~ normal(0,exp(2*logsig)) subject=pump;
run;
I'm able to get pe, p2, p4, p6. But not p3 or p5.

Am I pointing in the right direction?