A CHARADE is a type of word puzzle in which the answer is broken up into syllables or other parts of the words making up the answer - as in the party game.

1)
              My first beneath
            my second is seen,
     And moves at pleasure there;
 My whole an arch of beauty stands,
       supported by - not a trace - 
          to grace a pretty face.

2)
      My first is found in many mines;
             And there my costly
                 second shines.
    As for my whole - what shall I say?
        It seems intended to betray.

Answers:

1. Eyebrow
2. Stratagem

Credit: GAMES/World of Puzzles
January, 2016
Sam Loyd (1841-1911)
(#1: modified)
(#2: shortened)