In Powell v. McCormack (1969), the Supreme Court placed limitations on Article I, Section 5 of the Constitution. That article states:
Each House shall be the Judge of the Elections, Returns and Qualifications of its own Members, and a Majority of each shall constitute a Quorum to do Business; but a smaller number may adjourn from day to day, and may be authorized to compel the Attendance of absent Members, in such Manner, and under such Penalties as each House may provide.
This had previously been interpreted with great leeway, allowing the separate houses to refuse to seat members even for differences of political opinion. With Powell, Chief Justice Earl Warren wrote in the majority opinion that the House of Representatives was limited to only considering the enumerated qualifications of holding office as specified in Article I Section 2:
Therefore, we hold that, since Adam Clayton Powell, Jr., was duly elected by the voters of the 18th Congressional District of New York and was not ineligible to serve under any provision of the Constitution, the House was without power to exclude him from its membership.
Powell is about the refusal to seat an elected representative and not a Senator, but I believe most courts would extend that case's applicability to the Senate as well. This may not hold true, however. Because of this I believe the answer to your question is no, the Senate may not refuse to seat a duly elected Senator after the election results are certified. They could always try, but the Senator-elect would have redress through the courts and be able to point to a previous Supreme Court decision as precedent.
After the body has sat the Senator, they do however have much wider latitude for expelling them.