You probably can get to Vardø by boat as well, as I came by car, I only used the local boat to get to the little island of Hornøy.
Even that it is actually an island, you can get to Vardø by car as there is tunnel under to sea. Here is my car in front of the B&B
If you travel to Vardø by car you have to drive the 2890 meter long tunnel located 88 meters under sea level !! You can also travel by ship as the town of Vardø is located on a island.