Here's a link on proper canning from the USDA

and

Here's a link to the CDC to scare your pants off

Now rosemary, being sturdier than basil, MAY survive a sterilization process. You'd have to basically FRY the rosemary at 300 degrees for 2 hours to make sure no spores survive (just ONE botulism spore can divide and grow and make enough toxin to put you six feet under).

But my advice is always to make herb-flavored vinegar or alchohol, not oil.

Sterilization at home can be accomplished but it really diminishes the flavors and without proper equipment is tenuous, at best.

When I've wanted to give herbal oils as gifts, I put just the oil in a pretty bottle and dried herbs in a small container with instructions how to make it. Always included in the instructions is the admonition to refridgerate and use it within three days.

Martie

Food Science: Are Flavored Oils Safe?
A test cook recently needed to make garlic oil ahead of time but first
wanted to check for safety. Our consulting food scientist confirmed
that garlic oil must be refrigerated and even then used within a few
days. Oil creates a favorable anaerobic (absence of air) condition
that encourages any botulism present on the garlic to grow.
(Commercially sold garlic oil contains an acidic additive that kills
any bacteria.) There is a similar, although smaller, risk for
herb-flavored oils (herbs have fewer nutrients than garlic for
bacteria to feed on). If you're considering giving a homemade
condiment for a gift, flavored vinegars are a better bet--the
vinegar's natural acidity kills harmful bacteria, making them safe at
room temperature.