Nejimaki Seirei Senki: Tenkyou no Alderamin is a 13 episode anime series based off a currently publishing novel series. Odds are, you already have realized a couple things, but if not here they are now: First, this series tidies up an arc at the end, but it otherwise has an open ending. Second, odds are there won't be a second season; if lucky, there will be an OVA in the future, but it likely won't even be that. So, if these two factors are a big deal, you may want to wait on watching the series. If you don't mind, continue reading for a more detailed review.
The anime is essentially composed of a few sections, which each section tidying up neatly, while still being open to the next section. This allows the anime to flow nicely, though unfortunately, also leaves the series with a somewhat open ending; though the arc is tidies up, the viewer is left knowing that much is to follow along with foreshadowing, and it just isn't covered. Granted, anime based off of light novels serve not just to gather and entertain viewers, but to serve as an advertisement of sorts for the novel series, so this is to be expected.
As for the specifics, while the whole premise isn't made entirely clear, enough information is given to where the viewer won't dwell on the lack of information; also keep in mind, it's common for lots of details to miss making it from the novel series to the anime, so for minimal omission to seem apparent is pretty good on the anime's part. The setting seems to be perhaps a fantasy enlightenment period, with the main contrast being the female military uniforms, which have leggings and school skirts (since how could any anime girl not wear a pleated skirt as part of her main outfit?). Though the fantasy element is light, involving only the use of spirits (which some scenes may have you wondering whether they are fantasy or more sci-fi), the implementation of the spirits in the series adds to the fantasy feel.
What can I say? It's not terrific, nor experimental, but it's clear and crisp. Nothing to wow over, but nothing to complain over either.
The voices suited the characters well I feel. The opening and closing also fit the series. The series does a good job overall with using music in scenes, though there were a couple times where it bordered annoying for me.
While the main characters fall into stereotypes, they were portrayed well, to where they helped the story. A few of the characters remained rather static, while a few of the others grew over the course of the anime, which fit into the character types. The series also does a good job in reminding us that the characters are in a war.
This series had a mix of my favorite genre, favorites character types, and was based of a novel series so I started watching it expecting to highly enjoy it; thankfully, for me at least, it met my expectations.
Overall, I give this series a 9. I can see someone who's into "typical" shounen anime finding this series slow and boring, so if fast-paced action is what you're looking for, this series may not be for you. While this is a fantasy military anime, this is of a totally different strain than, say, the Gundam series. If you enjoy seeing what happens behind the action in war scenes, with action scenes involving character's planning counter-actions as much as actual action, this series is one you'll likely enjoy. If a semi-open ending is something that will bug you, you'll have to personally decide whether it's worth watching; if you enjoy this series, by the end you'll be wishing the light novels were being published by Yen Press. Hope this helped!