According to Information Please:

In the early days electors were most often chosen by the state legislatures, but with the growth of democratic sentiment popular election became the rule. After 1832 (and until the Civil War) only in South Carolina did the legislature continue to choose electors. In some of the states at first the people voted for electors by congressional districts, with two being elected at large from the whole state, but with the growth of political parties this plan was largely discarded (only Maine and Nebraska currently use it) in favor of the general-ticket system (the one now prevailing), whereby a party needs only a plurality to carry the whole state. Thus in most states a voter casts a ballot for as many electors as the state is entitled to. There is nothing in the Constitution that requires either that the electors be chosen by popular vote or that the general-ticket system be employed.

So Nebraska and Maine went back to the Congressional District method. It's not a holdover:

During the 1800's, two trends in the States altered and more or less standardized the manner of choosing Electors. The first trend was toward choosing Electors by the direct popular vote of the whole State (rather than by the State legislature or by the popular vote of each Congressional district). Indeed, by 1836, all States had moved to choosing their Electors by a direct statewide popular vote except South Carolina which persisted in choosing them by the State legislature until 1860. Today, all States choose their Electors by direct statewide election except Maine (which in 1969) and Nebraska (which in 1991) changes to selecting two of its Electors by a statewide popular vote and the remainder by the popular vote in each Congressional district.

Here's Maine's statute:

Title 21-A: ELECTIONS

  Chapter 9: CONDUCT OF ELECTIONS

    Subchapter 5: PRESIDENTIAL ELECTORS

§802. Representation

One presidential elector shall be chosen from each congressional district and 2 at large.

And here's Nebraska's:

32-714

Presidential electors; vacancies; how filled; meeting; procedure.

The Governor shall provide each presidential
elector with a list of all the electors. If any elector is
absent or if there is a deficiency in the proper number of
electors, those present shall elect from the citizens of the
state so many persons as will supply the deficiency and
immediately issue a certificate of election, signed by those
present or a majority of them, to the person or persons so
chosen. In case of failure to elect by 3 p.m. of such day, the
Governor shall fill the vacancies by appointment. After all
vacancies are filled, the college of electors shall proceed with
the election of a President of the United States and a Vice
President of the United States and certify their votes in
conformity with the Constitution and laws of the United States.
Each at-large presidential elector shall cast his or her ballot
for the presidential and vice-presidential candidates who
received the highest number of votes in the state. Each
congressional district presidential elector shall cast his or her
ballot for the presidential and vice-presidential candidates who
received the highest number of votes in his or her congressional
district.