If the U.S. Supreme Court reverses Roe v. Wade (1973) and Planned Parenthood v. Casey (1992), a number of American states will immediately criminalize abortion. Some of those states may also attempt to ban women from traveling out of state for the purpose of obtaining a lawful abortion elsewhere. But any such anti-abortion interstate travel ban would be constitutionally defective for multiple reasons.
First, the Constitution protects the right to travel, which necessarily includes the right to interstate travel. This is a fundamental constitutional right that has been repeatedly recognized by the courts. During the debates over the ratification of the 14th Amendment, the right to travel was invoked as one of the privileges or immunities of citizenship that the amendment was designed to protect from state infringement. For a state to prohibit (or even penalize) the act of leaving that state and doing something perfectly lawful in another state would violate this constitutional safeguard.
Second, an anti-abortion interstate travel ban would run afoul of the Dormant Commerce Clause, a legal doctrine which holds that the Commerce Clause, in addition to authorizing congressional regulation of economic activity that occurs between the states, also forbids the states from enacting their own interstate economic barriers.
James Madison explained the reasoning for this doctrine in Federalist No. 42. One of the main purposes behind the Commerce Clause, he wrote, was to clear away the various tariffs, monopolies, and other interstate barriers that the states had erected under the Articles of Confederation. In other words, one of the objectives of the Commerce Clause was to help create what we might today refer to as a domestic free trade zone. "A very material object of this power," Madison wrote, "was the relief of the States which import and export through other states from the improper contributions levied on them."
Abortion would count as an economic activity for Dormant Commerce Clause purposes. This means that a state barrier which interferes with the ability of a state resident to take advantage of another state's economic activity (abortion) via interstate travel would be constitutionally deficient under the Dormant Commerce Clause.
Finally, there is relevant case law which cuts against the lawfulness of any anti-abortion interstate travel ban. In Planned Parenthood of Kansas v. Nixon (2007), the Missouri Supreme Court reviewed a state law which created a civil cause of action against any person who helped a minor obtain an abortion without parental consent either inside the state or in another state. "Of course, it is beyond Missouri's authority to regulate conduct that occurs wholly outside of Missouri," the Missouri Supreme Court observed, and the law at issue "cannot constitutionally be read to apply to such wholly out-of-state conduct. Missouri simply does not have the authority to make lawful out-of-state conduct actionable here, for its laws do not have extraterritorial effect."