Don't lose your Google juice when you rename a file. Do not use META refresh to redirect pages - "301" code is the most efficient and Search Engine Friendly method for webpage redirection. There are different ways to implement and it should preserve your search engine rankings for that particular page. If you have to change file names or move pages around, always use the code "301", which is interpreted as "moved permanently".
Any time you move a page or just delete a page you should add a "301" redirect to a new page or a page for missing pages.
<% Response.RedirectPermanent("NEW PAGE URL HERE") %>
Although this works well it is difficult to manage the list of redirects and you need to keep the page around.
Note: If you are using a source control, like TFS, lock the old file so no-one can edit it by mistake.
WordPress automatically redirects posts when you change the URL (permalink). No further action is required.