Corroborating evidence is evidence that tends to support a proposition that is already supported by some evidence. For example, W, a witness, testifies that she saw X drive his automobile into a green car. Y, another witness, testifies that when he examined X's car later that day he noticed green paint on its fender.
For more information on this type of reasoning see casuistry.
Another type of corroborating evidence comes from using the Baconian method,i.e. the method of agreement, method of differences, and method of concomitant variation.
These are followed in experimental design. They were codified by Francis Bacon, and developed further by J.S. Mill and consist of controlling several variables in turn to establish which variables are causally connected. These principles are widely used intuitively in various kinds of proofs, demonstrations and investigations, in addition to being fundamental to experimental design.
See also: Judgment