I'm assuming that you're referring to the animal's death and the grief that is experienced in that particular guardian. Longitudinal studies will be hard to come by as the funding has yet to show up do much of this form of research. Look at the journal Anthrozoos for potential articles. Much of the work I've been exposed to relies and follows the findings from psychology, as this seems to be your focus (humans). You may want to contact your local SPCA or Humane Society for who they refer to for this type of service to get a better handle on current best practices.
I would start out with the Hosey & Melfi review listed below then branch out from there.
Davis, H. L. (2011). Death of a Companion Animal: Understanding Human Responses to Bereavement. In C. Blazina, G. Boyra, & D. Shen-Miller (Eds.), The Psychology of the Human-Animal Bond (pp. 225–242). Springer New York. Retrieved from http://link.springer.com/chapter/10.1007/978-1-4419-9761-6_13
Hosey, G., & Melfi, V. (2014). Human-animal interactions, relationships and bonds: a review and analysis of the literature. International Journal of Comparative Psychology, 27(1). Retrieved from http://escholarship.org/uc/item/6955n8kd#page-1
Smith, A. (2012). Pet Loss and Human Emotion: What's New? Death Studies, 36(3), 292–297. doi:10.1080/07481187.2011.590443
Weisman, A. D. (1990). Bereavement and Companion Animals. OMEGA--Journal of Death and Dying, 22(4), 241–248. doi:10.2190/C54Y-UGMH-QGR4-CWTL
There is an organization called The Human Animal Bond Research Initiative (HABRI) that specifically focuses on research and education in this area. You can find their website here: http://habri.org/