Grace McComas, a Glenelg High School student, committed suicide on Easter Sunday last year, after repeated cyberbullying through social media websites.
Sen. Allan Kittleman, a West Friendship Republican, sponsored the Senate version of the legislation.
Kittleman said this bill was "one of the most important pieces of legislation" that he has worked on during his eight years in the Senate.
"This is landmark legislation for Maryland," he said.
Under the law, bullying someone under the age of 18 through a computer or smartphone could warrant up to a $500 fine or up to one year in prison.
Kittleman said he expects the law to be a proactive tool for law enforcement.
He believes once someone is confronted with the possible charges by law enforcement, they will end their bullying.
Delay on stormwater fee fails
A proposal sponsored by Howard County Sen. Ed Kasemeyer that would have delayed the implementation of stormwater fees until 2015 passed the Senate Monday, but never received a vote in the House.
Kasemeyer said residents shouldn't have to pay the fee on top of the gas tax increase July 1 as the state still recovers from the recession.
"Most importantly, it's a lot of money for most people," he said.
Kasemeyer said he is not opposed to the stormwater fee, but the public has not been given much notice that the fee is coming this year.
"I just think it's a lot for the average person to absorb at one time," he said.
Kasemeyer said he "didn't quite understand the lack of interest in the House" on the bill.
The Senate voted to approve the bill 34-13.