The poet asks his Muse what recompense she can offer for her extended silence and apparent neglect of both poet and beloved.
Means both reparation and compensation, with implicit temporal urgency—what can the Muse do now to repair her negligence of the past?
By Sonnet 101, the three-way relationship becomes explicit: the Muse must inspire the poet, the poet must praise the beloved, and the beloved's beauty must justify the entire chain. If the Muse defaults at any point, the system of immortalization collapses. Shakespeare suggests that lyric poetry is not a private meditation but a public duty—the beloved deserves to be praised eternally, the poet deserves inspiration, and the Muse owes both her gifts.
'What shall be thy amends?' asks what compensation the Muse can offer for her default. Critically, 'amends' suggests time-based reparation—compensation for lost moments. The sonnet's urgent tone stems from the awareness that beauty fades inevitably with time, and only the Muse's power—working through the poet's verse—can arrest time's destruction. Every moment of the Muse's silence represents an irretrievable loss.
A musician asking their agent, 'What are you doing to promote my work?'—when really both artist and agent know the real question is whether art can ever be enough, whether fame or praise can ever match the thing itself.