Novels in which modern characters travel into alternate worlds, and all the magical action takes place there (except for the portal required to transport them), are thus not considered contemporary fantasy.
Contemporary fantasy is also to be distinguished from horror fiction, which also often has contemporary settings. When encountering magical events and creatures, the protagonist of a horror novel is horrified, while the protagonist of a fantasy novel (contemporary or otherwise) is filled with a sense of joy and wonder. Horrifying events may happen, but the fundamental distinction is vital.
Contemporary fantasies often concern places dear to their authors, are full of local color and atmosphere, and attempt to lend a sense of magic to those places.
Charles Williams, whose 1930s novels are mostly set in London, is called the father of contemporary fantasy. More recent notable authors include Charles de Lint (who uses a disguised Ottawa, Ontario as a setting) and Tim Powers (whose novels in this subgenre are mostly set in California). Other particularly notable contemporary fantasy novels include War for the Oaks by Emma Bull (set in Minneapolis, Minnesota) and The Folk of the Air by Peter S. Beagle (set in a disguised Berkeley, California). Neil Gaiman's American Gods and Neverwhere are also good examples of contemporary fantasy.
Superhero fantasy typically is set in contemporary times as well.