You don't mention where they lived or visited on either side of the journey you know about, so I can't make more specific suggestions about what to try. However, in my own research, I have found clues and references to international travel in City directories, social news columns in newspapers (I've had the most luck on Genealogy Bank, but the success rate for online searching is highly dependent on what area you need and what happens to be online) and in US Passport Applications.
NARA recommends the following search strategies:
To effectively and efficiently use passport application records, the
researcher should identify the persons who traveled overseas and the
approximate years of travel. The researcher should not automatically
assume an individual never traveled overseas, because, as indicated
above, foreign travel in the nineteenth century was more common than
one might expect.
Since passports were generally valid for two years or less, the
researcher should search the indexes covering the individual's entire
lifetime because he or she may have submitted several applications.
Multiple applications by the same person may provide conflicting, but
useful, clues for further research.
See also NARA's caution under "Limitations":
Passports were recommended, but not required, by President Woodrow
Wilson's Executive Order 2285 of December 15, 1915, which stated that
all persons leaving the U.S. should have passports.
For a presentation about how to find a Passport Application and what you can expect to find in the records, see NARA's YouTube Channel:
Passport Applications, 1795-1925.
1911 may be too early to find an application, but that doesn't mean it isn't worth looking. Some of the records are available online via FamilySearch: see United States, Passport Applications (FamilySearch Historical Records) and the companion Known Issues article.
Once you narrow down the possible travel dates, and perhaps find the preferred ship company from later passport applications, sites like The Gjenvick-Gjønvik Archives might yield other clues.
A recent post on the Genealogy Bank blog has a case study with tips on how to search by ship's name: My Ancestor’s Trip to America: Newspapers Tell the Story.