See this inheritance diagram of lettering styles. Many of them were used in manual writings on pergament or paper.
The image is grabbed from Wikipedia article "Insular Script"
Medieval writing is the main content of the next website: http://medievalwriting.50megs.com/writing.htm Check it!
Of course, computer fonts are modern creations, but you can surely find interesting ones by using those lettering system names as search tags. For example tag "Uncial" , maybe combined with "Roman" or "Celtic" or other limitation gives plenty of result in font selling or distributing sites. Here's a couple of results:
Fonts like these are often created by enthusiasts. They can give it for free for personal purposes, but anything else needs a separate written agreement. Always check the license!
How much they resemble some really existing old handwriting? You must decide it by yourself. Many of them surely have virtually nothing ancient.
To get a little more handwritten script look it's quite simple to detoriate perfect computer fonts by postprocessing an image which contains some writing. You can add variation to the geometry, color and the solidity of the edges. A programmer could write a "humanizing" script which adds placement and size variations when the text is still text, not an image.
The following image is an elementary example of detoriation (the text is taken from Wikipedia):
Handwriting contains often some extra long thin strokes at the ends of the letters. They make the letters effectively higher than in our normal modern fonts. In the detoriation example all letters are stretched vertically for that reason.
NOT ASKED: For really high quality results get a lettering artist who manually writes your texts. You need also proper decorative graphics and drop caps.