The Collaborative International Dictionary of English v.0.48:

Eminence \Em"i*nence\, n. [L. eminentia, fr. eminens eminent:
   cf. F. ['e]minence.]
   1. That which is eminent or lofty; a high ground or place; a
      height.
      [1913 Webster]

            Without either eminences or cavities. --Dryden.
      [1913 Webster]

            The temple of honor ought to be seated on an
            eminence.                             --Burke.
      [1913 Webster]

   2. An elevated condition among men; a place or station above
      men in general, either in rank, office, or celebrity;
      social or moral loftiness; high rank; distinction;
      preferment. --Milton.
      [1913 Webster]

            You 've too a woman's heart, which ever yet
            Affected eminence, wealth, sovereignty. --Shak.
      [1913 Webster]

   3. A title of honor, especially applied to a cardinal in the
      Roman Catholic Church.
      [1913 Webster]

U.S. Gazetteer (1990):

Eminence, KY (city, FIPS 24904)
  Location: 38.36538 N, 85.17432 W
  Population (1990): 2055 (925 housing units)
  Area: 4.2 sq km (land), 0.0 sq km (water)
  Zip code(s): 40019
Eminence, MO (city, FIPS 22276)
  Location: 37.14627 N, 91.35853 W
  Population (1990): 582 (303 housing units)
  Area: 2.5 sq km (land), 0.0 sq km (water)
  Zip code(s): 65466

Moby Thesaurus II by Grady Ward, 1.0:

169 Moby Thesaurus words for "eminence":
   Olympian heights, VIP, acme, aerial heights, altitude, apex,
   ascendancy, august, authority, bas-relief, bellying, big-name,
   big-time, big-timer, bigwig, boldness, bulging, ceiling,
   celebrated, charisma, charm, chief, clout, consequence,
   conspicuousness, control, credit, dignitary, dignity, distinction,
   distinguished, dizzy heights, dominance, dominant, domination,
   effect, elevation, embossment, eminent, enchantment, esteem, ether,
   exaltation, exalted, excellence, excrescence, excrescency,
   extrusion, fame, famed, famousness, favor, force, gibbosity,
   gibbousness, glory, good feeling, grandeur, great, greatness,
   hauteur, heaven, heavens, height, heighth, heights, heroism,
   high mightiness, high relief, highness, hold, honor, illustrious,
   illustriousness, importance, important, incidental power,
   influence, influentiality, influentialness, insinuation, kudos,
   leader, leadership, leverage, lift, lion, loftiness, lofty,
   low relief, luminary, magnanimity, magnetism, majesty, mark,
   mastery, memorability, moment, nobility, noble, notability,
   notable, note, noteworthiness, outstandingness, peak,
   perpendicular distance, personality, persuasion, potency, power,
   precedence, predominance, preeminence, preeminent, preponderance,
   prepotency, pressure, prestige, priority, projection, prominence,
   prominent, protrusion, protuberance, protuberancy, purchase, raise,
   rank, reign, relief, remarkableness, renown, renowned, reputation,
   repute, rise, rising ground, rule, salience, salient, say,
   seniority, significance, sky, stature, steep, stratosphere,
   suasion, sublimity, subtle influence, suggestion, supereminence,
   superiority, supremacy, sway, tallness, toploftiness, tuberosity,
   tuberousness, upper hand, uprise, vantage ground, vantage point,
   weight, weightiness, well-known, whip hand, zenith