There's a non-trivial difference between a logo and brandmark. A brandmark is implicitly connected to business strategy, brand narrative and other assets. Logo design requires only entry level design skills. If you do not need a complete brand identity solution then you're probably better off sourcing logo designers via the following websites.
If you'd like to consider a more integrated approach to your brand identity then consider the following two options.
If you're looking for this particular combination then your primary requirement is probably a website and – on this basis – a logo is also required. A logo is an entry level brand identity and doesn't warrant the attention of a branding specialist. If you only need a logo in addition to a website then you're probably better off sourcing suppliers that can be found via the following websites.
If you'd like to consider a more integrated approach to your brand identity then consider the following two options.