It depends on the used type size. It should be good visible for common eyes. So its big on 9pt and very big if you set smaller text. On larger text sizes it becomes smaller. So you should choose a size for what your design best fits for - mostly body text or display.
I think the R in the registered sign should have the same size (caps high) as the TM mark - but maybe it depends on personal taste. I see very often a different approach.
Lots of fonts don't care much about such issues and use a standard sign and size.
my suggestions to start from:
(percentage of the caps high)
4-8pt: bigger
9-12pt: 55 - 47%
16-28pt: 45 - 40%
--astype.de--