Hi there,
I'm a medievalist in English who got admitted to a few schools this season. Here's my advice:
First, show some initiative. What really helped me out, I think, was my self-motivated language study. I don't actually have Latin (a big plus for any candidate in medieval) but I had Greek, Old English, Middle English, and reading knowledge in a bunch of others. At once school, on my visit I was referred to as the 'autodidact.' I think that's a big reason why I got into that school. Since most undergraduate programs don't have the most rigorous medieval program, and since most graduate programs don't have super-extensive course offerings in medieval, market yourself as a self-starter, someone who is going to thrive in a good program and make the program look great with minimal pampering.
Second: the writing stuffs. Your writing sample and personal statement need to be some of the best writing you've ever done. In my personal statement, I showed that I had done extensive research on the programs I applied to. In one statement for example (for one school I gained admission to), I listed the courses I would take to complete a dual master's in Medieval Studies. It's that kind of specificity that's going to make you stand out.
And third, take yourself seriously, and present yourself seriously. These programs get a whole bunch of half-hearted applications, sometimes from people who don't know what grad school is about. You can immediately distinguish yourself with just a touch of professionalism and self-confidence in your writing and communications with the school. Present yourself as a competent scholar and an affable colleague. Really own it; self-doubt tends to shine through in writing.
That's my two cents.