I see that Ellis Island passenger list differently; I see those particular Herman's as listed as US Citizens...look at the line in the middle across the top where it says: United States of America Citizen...it's when you get to passenger #14 [Eta Modest/Hodesh] that it switches to Germany/German - then mentions Fulda, etc. For passenger 15, [Kroes], we're back to "US Citizen". Passenger #14 has to explain where she's going as she's an 'alien' [see that column at the top far right] - the others (US citizens) don't have to list who they know in the US or where they're going.
What may help you to cut to the chase may be to go online and look up "Minnesota Official Marriage System (MOMS)" and order a copy of Fred & Emma's marriage certificate [#M7-100] for a cheap $9.00 + postage; MAYBE at the time they [the state or county] required birthdates, or parents names - I don't know. For a lousy 9 bucks, you might get lucky. Fred is listed there as Fred Charley BErnhardt (instead of BArnhardt) and Emma is listed as Emma Christina Herman; marriage date April 18, 1911, Wadena County.
If you look closely at the 1925 Iowa State Census, for Fred & Emma in Grant, Pocahontas [image 43], you'll see on the next page [image 44] where they ask each household member who their parents are, how old the parents are, and where the parents were born (and married). Fred lists John Barnhardt & Lena Lange; for Emma only her father's last name, Herman, is listed, and for her mother only the last name of "Delaffaf" is listed...whether that was spelled or transcribed correctly, who knows, but there's a clue as to her mother's maiden name. Maybe she didn't bother with her parents first names and ages because they were already dead...?? Or maybe whoever talked to the Census taker just wasn't sure.
According to that 1925 Iowa State Census, Emma claims she's age 33 - birth would be about 1892. I found a NY passenger list with an Emma Herman, age 18, single, born about 1891, listed as the niece of (transcribed by Ancestry as) "Carotens Terlefs", age 66, departed from Hamburg and arrived March 8, 1909 on the ship Kaiserin Auguste Victoria. On the manifest it states she's from Lunden, Holstein, Germany. Seems to list her father as Fritz (?) Herrman. On this passenger list she is an 'alien'. Looks like her Uncle is listed as Citizen of the U.S.A. with "non-immigrant alien" stamped there?? Did this Uncle go to Germany to bring his niece Emma to the US? Is that 'your' Emma? I DON'T KNOW....but birth year/arrival year are close. And gee whiz, this Emma is from the same neck-of-the-woods (Holstein) that Fred was from (Holstein)....
Back to the 1925 Iowa Census - she claims to have been in the country 16 years as of 1925 [1925-16=1909], and in the state of Iowa for 14 years [1925-14=1911]; it would be nice to find her in a 1910 Census. Since she married in 1911 in Verndale, MN, wouldn't be surprised if she turns up in a 1910 MN Census. It's hard to tell, but on that NY passenger list, that particular Emma (with her Uncle) has to list their destination in the US; state & city - hard for me to make it out...but does it look like possibly "Minn" and "Varndal" (for Verndale)?...but IF this is her (and I am NOT sure), finding her or that Uncle in a 1910 Census may help if that's who she stayed with until her 1911 marriage in Verndale, MN - again, IF that's your Emma...And even if it isn't, an Emma Herman should be showing up somewhere in a 1910 Census if she arrived in 1908-09.
I did find an Emma "Harrmann", born about 1893 Germany, working as a servant in the Yanz household in Staples (Ward 2), Todd County, MN, which is 11 miles right down I-10 from Verndale. Seems a couple years too young, but people fudged their ages sometimes...plus, depends on who gave the Census taker the info.
Not sure any of the above guesswork is right - it's just that - a guess. But there's some reason why a 17-18 year old girl would come to New York and end up in the boonies of MN of all places, and it would probably be because some type of relative was already there. [And maybe I'm way off here too.]
Personally, I think obtaining a copy of their marriage certificate would maybe help more; hopefully, it contains a birth date and/or parents names on it.