Further to Joel Weintraub's excellent comment recently (26 Feb 2019)
there is another point worth reiterating every few years, regarding
passenger manifests for ships arriving in New York between 1897 and
1903 (though I don't believe in this instance it's a possibility
because there exists a detention page).
The point is that (for this period) when a ship arrived at New York,
the manifest was literally torn in two. The section containing first
and second class passengers stayed with the ship when it docked in
New York. These passengers were checked by Customs staff as they were
not considered to be of 'immigrants' status (even if they were
immigrants). However, as we know, steerage class passengers were
barged over to Ellis Island (along with their portion of the manifest)
and inspected by immigration staff (not Customs).
The two portions were never "reunited", so that years later when the
indexing was carried out the first and second class passengers were
never indexed. Hence, if your ancestor was lucky enough to travel
first or second class, and immigrated between 1897 and 1903, this
could be the reason why you can't find them.
I know because this happened to me when my great grandmother's brother
Edward Prince, and his very recent bride of just a few days immigrated
from London to New York. (And no, I've not definitively located themvia the UK Outbound lists.)
This issue has been investigated even more thoroughly by Marian Smith,
Historian to the former Immigration and Naturalization Service.
Jeremy G Frankel
ex-Edgware, Middlesex, England
now Sacramento, California, USA
FRANKEL/FRENKEL/FRENKIEL: Gombin, Poland; London, England
GOLDRATH/GOLD: Praszka, Poland; London, England
KOENIGSBERG: Vilkaviskis, Lithuania; London, England; NY, USA
LEVY (later LEADER): Kalisz, Poland; London, England
PINKUS, Poland; London, England
PRINCZ/PRINCE: Krakow, Poland; London, England; NY, USA