I'd find it quite strange if a designer didn't have some kind of web-presence.
I'd have to agree here. I wouldn't expect much, just an intro and contact point to let them know they're in the right place plus a few examples of what you produce. Word of mouth often leads to your website, well it does in my case. Normally I get a mail through the site with something like "I got your name from 'Client' who said you might be able to help me with X". Just my 2 pence as always