Walk up from Am to Em same key possible?
 

I have written an instrumental for guitar(12 str) for a 500 year old song. Sort of medieval and very simple. I discovered the song itself is sung in Em, Am, G and D. The instrumental is in Am only, with various string choices and open notes. It starts and ends in Am, but I would like to use it and have it flow naturally into the introduction of the song(Em first chord). I don't mind if it's a string walk up and not the whole chord strummed.

The way it sounds now is not too objectionable, but as it is now I need to dead stop the Am chord, and "curtain raise" Em to the song in a one beat strum. The laps here is a bit awkward and it sounds too much like an intro.

I have heard some songs that do this and they still sound pretty good. I may just leave it the way it is. Perhaps, Em and Am are natural harmonics in the music world. But I find they are slightly off for a walk up.

Any tips would be appreciated. Thanks :)

What about a G major chord as tie in given that it is a common element in progressions containing Am and Em, or maybe, a C major (but probably less so).

Sounds like A Dorian? Perhaps use an intervening Bm chord.

What about walking the D string of the Em, on the second fret, to the forth fret and back down into the Am? Sounds pretty sweet to me.
You can even give it a little bit of vibrato while you're there at the forth fret.

I'm sorry, but I'm lost here. What's the problem? :)

Yeah, me too. Am is the IV to Em, and Em (or Em7) is the V for Am. Depending on what kind of scale you are using, a run up/down is simply a matter of following that scale in any direction.

Who says the key is Am? With 500 year old music (aka renaissance) I am thinking modal and also probably not using either a base line walk up or walk down.

A minor is the IV of the E minor, so it works fine.

I'd suggest trying a walk up from the A min Barre chord at the 5th fret up to the E min barre chord at the 7th fret. (it's the same shape as B min chord at 2nd fret just moved up the fretboard) It might work for you