In this letter, we propose joint quantization of the parameters of a set of sinusoids based on the theory of trellis-coded quantization. A particular advantage of this approach is that it allows for joint quantization of a variable number of sinusoids, which is particularly relevant in variable rate parametric audio coding. Under high-resolution assumptions and based on a perceptually relevant distortion measure, we derive analytical expressions for the optimal design subject to an entropy constraint. Numerical experiments show a significant performance gain compared to optimal spherical quantization at the cost of a slight increase in computational complexity.