The measure was titled the "Keep Your Health Plan Act," though the decision would ultimately lie with insurers about which policies remain available.
"This legislation is about providing folks the peace of mind that they will be allowed to keep their current coverage if they so choose," Upton said in a statement. He blasted President Obama for claiming that "if you like your plan, you can keep it" under the healthcare law.
The new bill comes as thousands of customers receive policy cancellations due either to ObamaCare or normal turnover in the individual market.
The Affordable Care Act requires health policies to provide a basic standard of coverage, and most that do not will be prohibited in 2014.
Supporters say the requirements enhance patients' healthcare, and that consumers whose policies are cancelled will receive richer benefits in their next plans.
ObamaCare also offers premium tax credits to make coverage more affordable for people with lower incomes.
The administration is under serious pressure to make its online enrollment site work for people who are receiving cancellation notices.
The Health and Human Services Department says it will make HealthCare.gov fully functional by Nov. 30, just two weeks before the deadline for enrolling in coverage that begins Jan. 1.