The bloc is keen to campaign against Lukashenka's autocratic regime, but it also wants to avoid being associated with any individual challengers or parties.
The answer, as it transpired over the course of the day, was to grant Milinkevich almost unprecedented levels of political access -- while keeping it all very quiet.
Milinkevich met with EU foreign-policy chief Javier Solana, External Relations Commissioner Benita Ferrero-Waldner, and European Parliament President Josep Borrell.
Most significantly, Milinkevich spent a half hour with the 25 EU foreign ministers -- a rare honor for any opposition figure. None of the meetings was accompanied by a press opportunity.
Ursula Plassnik, foreign minister of the current EU chair Austria, offered a cursory summary of today's deliberations on Belarus that followed the talks with Milinkevich.
She said the EU is very concerned about the situation in Belarus and considers the elections an "important yardstick."
"The OSCE has been invited to monitor the elections and we expect that, correspondingly, the observation mission is allowed to carry out its work in an unhindered manner," Plassnik said.
The EU ministers adopted a statement that repeated a threat made first in November to take "restrictive measures" if the 19 March elections are not free and fair.
Today's statement, however, added an important detail. The EU now explains that the measures will target "the responsible individuals" in any failure to "uphold international standards in the electoral process, in particular those of the OSCE." This means the treatment of the OSCE observers will be particularly crucial.
The EU has taken such measures before. A travel ban is in place against a number of officials considered culpable for the disappearance of opposition leaders, the obstruction of relevant investigations, or the mistreatment of demonstrators.
The EU statement today also stressed that Belarusian authorities must allow all eligible candidates to register, campaign freely, and to enjoy equal access to state-controlled media. Domestic and international media must also be able to report freely on the electoral process.
Milinkevich's role was largely to offer the EU ministers a chance to hear a firsthand account of the situation in Belarus.
Estonian Foreign Minister Urmas Paet told RFE/RL that Milinkevich provided a short overview, took questions, and then summed up his expectations.
"His message, briefly, was that where he most sees opportunities for the West to help [Belarus] today is by trying to pass on adequate information via radio and TV channels; and also keep the doors open to nonpolitical groups such as the young, sports people, and cultural representatives," Paet said.
The EU last week awarded a German-led media consortium a 2 million euro ($2.42 million) contract to broadcast independent radio and television news to Belarus, starting in February. The German international broadcaster Deutsche Welle has offered Russian-language radio programs since November. However, some Belarusian opposition figures have warned the programs will only reach a small minority of the Belarusian public.
Some EU member states, led by Lithuania and Poland, today pressed for the easing of EU visa restrictions against Belarusian citizens. Today's EU statement encourages the "facilitation" of contacts with Belarusian civil society, but easing visa rules is politically too sensitive a measure for most member states.
A few dozen members of the Belarusian diaspora in Belgium gathered on Monday within a stone's throw of the building that hosted the meeting of the 25 EU ministers. They carried placards likening Lukashenka to Stalin and Hitler and condemning Russia's support of his regime.
Zmitier Pimenau, the leader of the association of Belarusian refugees in Belgium, told RFE/RL that Russia's stance is key for the future of his country.
"The biggest threat for Belarus today is losing its independence and being occupied by Russia," Pimenau said. "We know that Lukashenka would not survive even for a day without Putin's support. And Russia channels large sums to support the dictatorship [in Belarus]. Putin has begun to terrorize with gas [supplies] not only Belarus but also all of Europe. This could be seen when he turned off the gas for Ukraine. Tomorrow the gas may be turned off for Poland, the Czech Republic, or Germany."
Pimenau said his organization represents about 1,700 Belarusian refugees in Belgium.
Milinkevich is expected to meet with members of the Belarusian diaspora in Belgium on 1 February.