Hi Chris,
I would try the running the Multiple Ring Buffer geoprocessing tool on your coastline feature and see if the output buffer polygon satisfies what you are looking for. This tool allows you to input multiple buffer values in a unit of measure that you define (e.g. 20m, 40m 80m, etc.) The buffer polygon will cover both the seaward and landward sides of the coastline feature and I'm pretty sure you would only want to see the buffer polygon around the landward side to show the sea level rise. However, if you have a separate feature layer for the sea level you could overlay it so the seaward side of the buffer polygon is covered, or you can use the editing tools to split the buffer polygons and remove the portion you don't need.
To start, I would open the help and perform a search on "Multiple Ring Buffer" and read up on the tool. Before running the tool, select only one coastline feature and see if the output buffer polygon is correct. I hope this helps.
Andy