How should the dimensions for a 805 MHz resonant rf cavity be
determined? This is a simple pancake cavity. I want the dimensions of
the cavity diameter and length.

This probably doesn't answer your question, but I hope it will be
helpful.

Mafia, Superfish, and HFSS (Ansoft Corporation) are mentioned often
for creating/checking the designs.

Electrodynamics Software
http://laacg1.lanl.gov/laacg/c-on-line/ed.html

Mafia
http://hpcf.nersc.gov/software/apps/electromag/mafia/

HFSS
http://www.ansoft.com

DESIGN AND FABRICATION OF AN 805 MHZ RF CAVITY WITH BE
WINDOWS FOR A HIGH RF POWER TESTING FOR A MUON COOLING EXPERIMENT
http://accelconf.web.cern.ch/AccelConf/p01/PAPERS/MPPH062.PDF
(Am I confusing "pancake" with "pillbox"?)

Resonant Cavity Design Using the Finite Element Method
http://accelconf.web.cern.ch/AccelConf/e96/PAPERS/THPG/THP137G.PDF