Generalized Estimating Equations and log-likelihood calculation

Is anyone aware of a way to calculate log-likelihood for GEE models?

No. GEE fitting is based on quasi-likelihood.

However, it is possible to derive AIC-like measures based on the 
quasi-likelihood. Lebreton et al (1992) suggested a simple adjustment in 
the GLM case, i.e. when using family=quasibinomal or quasipoisson. For GEE 
models, Pan (2001) has introduced QIC. None of these measures are 
implemented in R or in any add-on package as far as I know.

Henric