I have a sister who doesn't listen to much metal but quite likes it when she does (I think it's something about the energy and lead guitars mostly) and I'm looking for something to recommend to her. The only thing is that she really likes bagpipes and would probably totally dig something metal that has bagpipes in.

I personally haven't heard many songs that do include bagpipes and those that I have (Tyr, Gwydion) aren't really bands that I follow, so I'm not sure whether the bagpipes are a major feature or not. I guess many of these would be in the folk metal genre, since a lot of bands incorporate native instruments.

My need is thus for some recommendations about metal bands with bagpipes who play reasonably melodic material, preferably of a mid-paced or high-paced variety. My sister isn't really into death growls, so that would be a bit of a turn-off, as would anything too wacky or avant-garde. However, she never finds anything too cheesy, so don't hold back with bands you think are kind of bad.

I think there is bagpipe inNokturnal Mortum. Otherwise, the guitar sound in Amber Tears is strikingly similar to a bagpipe's, that's the impression I get anyway. Both bands use growls though, but not only.

Mediaeval metal is a thing in Germany (even if for some reason this site doesn't accept it as metal), where metal/hard rock/Neue Deutche Härte is mixed with mediaeval instruments, bagpipes often being a prominent part of the sound.
In Extremo are probably the best known, alongside Subway to Sally and Schandmaul, though the two latter are somewhat less metal-y than In Extremo. Corvus Corax is another well known band, they use traditional instruments exclusively but are still regarded as metal by many and they're often playing at metal festivals like Wacken and Summer Breeze.

Folkstone are the italian clones of the bands suggested by Pegster, pretty much bagpipe driven rock/metal

Eluveitie is the first one that springs to mind. More prominent on some songs than others, probably used most heavily on 'Inis Mona', although this song solely uses growls for vocals which you said might be a problem. Most of their stuff mixes female cleans and male growls. Perhaps some of their other songs might be more well-received?

https://www.youtube.com/watch?v=iijKLHCQw5o - 'Inis Mona'
https://www.youtube.com/watch?v=-w2m-TeLi6I - 'Call of the Mountains' (solely cleans)
https://www.youtube.com/watch?v=d-pSq4MJmy8 - 'Rebirth' (more flute than bagpipes)
https://www.youtube.com/watch?v=rfQmEIIkMFc - 'Slania's Song' (I would assume this to be the best fit from what you've described)

Saor from Scotland. They make great use of bagpipes, doesn't sound corny or cheesy at all.

Check out Moonspell's song "Trebaruna" from their "Wolfheart" album.

Grave Digger - Tunes Of War album, especially Rebellion (The Clans Are Marching) song

Apocalypse Orchestra - The End Is Nigh (Medieval Folk/Doom Metal)
There are (almost) clean vocals, but the music is probably slower than "mid-tempo".
https://www.youtube.com/watch?v=xxuPi5T_0zs

Good choice. Blind Guardian also has some bagpipes on "Somewhere Far Beyond".

The most recent two Nightwish albums have had prominent bagpipes.

Actually a completely non-metal recommendation here but justified because it opens with a fantastic bagpipe intro: Pragnavit -Svietacjam. Very skill- and tastefully done ambient album that should suck you in with said intro alone. Give it a try if you like to immerse yourself in "natury" and relaxing soundscapes by that largely unknown artist.

Ooh, OOh!

Arkona!

Not on every track but if you give them a good go then you will find some.

Off the top of my head...Pokrovy Nebesnogo startsa.

What's cool is they aren't Celtic at all; they're Slavic metal

And I think I remember...Celtica?

AC/DC - It's A Long Way To The Top If You Want To Rock N Roll