Many weddings in Japan imply a ceremony at a Shinto shrine. The whole affair is a rather formal and traditional one and includes a religious ceremony inside the actual building of the shrine, and very often a little procession with the priest and attendants, and of course a photo session with the whole family.
This is a great opportunity to see incredibly beautiful kimono and whole family fully dressed up in a traditional formal way. A polite request to capture a few photos is usually accepted with a smile. I never had a refusal! To witness a wedding, I think the best way is most probably to hang around one of the famous shrines in Kyoto on a weekend day.