The hardest contract to sign is the first.
Until you’re actually doing work for a client, your skill level and value are abstract notions; your sales tactics and supporting material won’t make your rates appear lower than they are. Seeing real results might.
If you see potential for repeat business with a client, reduce your fees on the first contract (lower rate or lower number of hours depending on what’s visible).
This will help establish the relationship, overcome the cost barrier and could be a great foot in the door (Robert Cialdini). Your regular costs won’t be an issue on following contracts once the value is demonstrated. This is tried, tested and true.