Health Care Market Certainty and Mandate Relief Act This bill appropriates such sums as necessary to pay through health care plan year 2019 the cost-sharing reductions authorized in the Patient Protection and Affordable Care Act. (A cost-sharing reduction is a discount that lowers the amount an individual pays for deductibles, copayments, and coinsurance; the federal government pays the difference directly to insurers.) The bill excludes payments to insurers that cover abortions other than abortions necessary to save the life of the pregnant woman or abortions of a pregnancy resulting from rape or incest. The bill amends the Internal Revenue Code to suspend for 2017-2021 the individual mandate to maintain minimum health care coverage. The bill suspends the employer health care mandate for 2015-2017, thereby exempting employers from penalties for failing to provide mandated coverage during that time period. The bill increases the monthly contribution limit for health savings accounts through 2022.