You may wish to limit your search to Shakespeare specific journals. Just remember, it's best to gather information from multiple sources, in order to have a wider angle on your research. The best way to search across a wide array of journals will be to use OMNI and/or one of the periodical indexes listed to the right.
Generally speaking you can use OMNI to find articles on Shakespeare's work. However we do have some periodical indexing tools not included in OMNI that you may wish to peruse, particularly if you doing a more comprehensive literature review. A periodical is any publication that is published regularly, such as a journal, a magazine or a newspaper. A periodical index/database allows you to search the contents (i.e., articles) of journals, magazines and newspapers to find articles on a particular topic, by a particular author, or by a particular title.
To find scholarly literary journal articles, aside from OMNI, the most useful databases are:
World Shakespeare Bibliography
Provides annotated entries for all important books, articles, book reviews, dissertations, theatrical productions, reviews of productions, audiovisual materials, electronic media, and other scholarly and popular materials related to Shakespeare and published or produced since 1900.
MLA International Bibliography (via Proquest)
The MLA International Bibliography provides a classified listing and subject index for scholarly books and articles published on modern languages, literatures, folklore, and linguistics. Each year more than 50,000 items are added. Coverage is from 1963 to the present.
On the Basic Search screen, limit your search by placing Shakespeare into the Author as Subject field, or type the title of your play or plays into the Author's Work field. Then use the keyword box to narrow your search further by character, theme, topic, etc.
ITER: Gateway to the Middle Ages and Renaissance
Iter's bibliography covers all literature pertaining to the Middle Ages and Renaissance (400-1700). Citations for journal articles, reviews, review articles, bibliographies, catalogues, abstracts and discographies are included. Also included are citations for monographs, and material published in monographs and collections of essays. Not all articles are in English.
Other guides that may be useful to your work include: