I've been researching this recently... I don't have a 6820 yet, and in fact, the phone purchase is going to be contingent on a Mac solution being available.
The 6820 is a Nokia Series 40 platform phone, and as such isn't supported by Apple's iSync (either by v1.5 in Panther or v2.0 in Tiger), unlike the Series 60 platform devices.
There are a couple of 3d-party utilities that may be compatible with it:
1) DataPilot For Mac (http://www.susteen.com/mac_features.htm); it allows moving Address Book & iCal records to/from the phone. They explicitly claim 6820 support.
however, it's apparently not an automatic sync (meaning, it doesn't know whether the computer-side DB or phone-side DB has changed, so you have to manually decide which records go in which direction). Also, their solution only works with a USB cable, not Bluetooth (not quite clear which cable, as the common Nokia DKU-5 cable apparently doesn't usually work with Macs, and the newer CA-42 cable is needed). They don't have a demo, and they haven't responded to e-mail inquiries yet.
2) OnSync, (http://www.onmadesoft.com/), is for Address Book entries only (no iCal support) , and is a $12 shareware; looks like it has semi-automatic detection of changed records, and you can specify which AddressBook category get's synced, as well as what do to in various phone/Mac record format mismatches. There's a demo mode, but it's fairly limited. I've gotten it to see my Ericsson t39m phonebook (via Bluetooth), but not suceeded in actually moving any record in any direction. I've also had one app crash & a couple of odd error messages & behaviors with it, despite having experimented very little, so I'm not sure how stable it is.
The site says contacts with multiple numbers aren't yet supported on Nokias, and only mentions the 6800 specifically, but if the 6800 works, I suspect there's a good chance the 6820 will as well.
I've contacted the developer and will update here if I learn anything new.