"stepped up measures" is correct and can be used in written English.
You can use it when you want to express the idea of an increase in the intensity of an action, such as increased security, increased efforts, or increased discipline. Example sentence: The country has implemented stepped up measures to ensure its citizens' safety in the midst of the COVID-19 crisis.
Western counterterrorism officials have acknowledged the threat and European intelligence agencies have reportedly stepped up measures to track recruits.
In addition, American and NATO forces have stepped up measures intended to stop insider attacks, including rules about not being alone with Afghan soldiers.
The government and its allies have stepped up measures against the country's drug trade, worth about $3 billion dollars annually, which experts say helps finance the Taliban.
The Turkish government claims that it is fully committed to defeating Isis and the Suruc attack may even have been in retaliation for stepped up measures against the movement.
Prime Minister Wen Jiabao of China called for stepped up measures on Tuesday to prevent and control any possible cases of swine flu that might show up in the country.
To remain in the present favourable situation, stepped up measures will be needed, to identify imported cases, to control domestic outbreaks and to prevent transmission within the health-care sector.
Some expect inflation to moderate later this year, as the government steps up measures to lift production and distribution of food.
On Thursday Austria announced it was ready to step up measures to discourage people from making the journey to Europe from countries such as Afghanistan, Iraq and Syria.
Health officials say they are stepping up measures to stop the flu here, but some Aboriginal leaders and health activists say it is not enough.
This echoes assessments from many other economists, many of whom expect the Chinese authorities to step up measures to contain bank lending, including nudging up interest rates again later this year.
In China, weak external and domestic demand continued to weigh on the manufacturing sector in March, a survey released Thursday showed, raising expectations that the Chinese authorities would step up measures to revive economic momentum.
