First of all, tempo had to be moderate to slow with no virtuoso or dance elements. Rhythms which evoked very dramatic emotions, sudden action, such as sharp dotted rhythms or figura corta (eighth note and two sixteenths) were not used in such pieces.
Melody had to be singable without any association with instrumental music. Phrasing was largely natural which often subdivided the piece into symmetrical units. Harmony was used quite colorful with nice modulations, chromatic chords and sequences as well as frequent major-minor mode borrowings.
Registration and dynamics focused on soft to medium sounds (strings, flutes, perhaps one or two principals, sometimes a soft reed).
Such a piece for today's sight-reading is Elevazione (p. 3), Op. 120, No. 2 by Luigi Bottazzo (1845-1924), a Romantic Italian organist and composer. This piece was intended to be performed for Elevation section of the Mass (in those days, organist played organ music during Elevation (after the Benedictus).
By the way, this composition is a wonderful exercise for the use of the swell pedal (for the right foot). In places where there are crescendo and diminuendo markings, avoid playing the bass part with the right foot. Observe that the swell motion is gentle and natural enough without too sudden and too powerful changes in dynamics. On modern organs, Italian Organo Espressivo could mean Swell and Grand Organo - Great.