Typing the full journal name followed by the word abbreviation into a Google search will bring up the abbreviation with a strict ISO4 notation. Caveat, they come up with a full stop (period) on each abbreviated word, which is not what every journal uses.
Journals in NCBI Databases.
Information in this free database includes publisher, frequency, abbreviation, ISSN, and whether indexed in MEDLINE. Since the NCBI databases cover more than just medicine, this source is useful beyond the health sciences. However, it includes only currently active titles.
A database containing information on nearly 100,000 journal titles, including description (aims and scope), abbreviation, homepage, and ISSN.
This catalog gives you full information on all their indexed journals, including the abbreviation.
PubMed displays the correct journal abbreviation in the article information.