A laser machining system is used to precision laser drill holes in an elastomeric material, preferably silicone rubber, to form holes to support miniature electronic components temporarily while they are being processed or tested. The holes are formed by directing laser pulses from a laser to a top surface of the elastomeric material in a plurality of passes in a direction proceeding from a non-zero inner diameter to the desired diameter or from the desired diameter to the inner diameter. The plurality of passes forms a first pattern such that a successive pass of the plurality of passes overlaps a previous pass of the plurality of passes. The first pattern is repeated without changing direction or the first pattern is repeated while reversing the direction until the hole is formed through a bottom surface of the elastomeric material.