The more effort that’s put into finding the right designer, the more likely clients will be to get the level of design they deserve. As I’m not always the right fit for the projects I’m approached about, whether due to budget or skillset, I’ve collated a few broad resources that I hope are helpful.

Creative Review. One of the design profession's leading publications.
Behance. A portfolio network where designers show-off their skills.
LinkedIn. Allows designers to display their Behance portfolios on their LinkedIn profiles.
THE DRUM. News, information, jobs, a comprehensive directory, and more.
FormFiftyFive. Design inspiration from around the world.
AIGA. US-centric, but designers and clients don't need to be in the same country.
Graphic Artists Guild. Similar to AIGA, I think, only smaller.
Twitter. You could search for a relevant term, or ask someone to post a request.
Identity Designed. Brand identity case studies from designers across the globe.
Dribbble. A "show and tell for creatives."
Forrst. Similar to Dribbble in some ways.
Coroflot. Portfolios showcasing a wide range of creative specialities.
Creativepool. Jobs, portfolios, and freelancers.
Design Week. A professional publication with news and features.
Cargo. A popular portfolio platform with a "featured sites" showcase.
Graphic BirdWatching. Promotion of female graphic designers everywhere.
Design blogs. Those are just a few of the ones I like visiting.

Additionally, it can be a good idea for potential clients to contact companies that have distinctive branding, as there’s no harm in asking who created the work. Designers, too, can be a great source of referrals, as those I know are more than happy to recommend others in the design profession.

Further resource: Design Business and Ethics, from AIGA.