While subjective assessments have been the gold standard for evaluating speech generation, there is a growing need for objective metrics that are highly correlated with human subjective judgments due to their cost efficiency. This paper proposes reference-aware automatic evaluation methods for speech generation inspired by evaluation metrics in natural language processing. The proposed SpeechBERTScore computes the BERTScore for self-supervised dense speech features of the generated and reference speech, which can have different sequential lengths. We also propose SpeechBLEU and SpeechTokenDistance, which are computed on speech discrete tokens. The evaluations on synthesized speech show that our method correlates better with human subjective ratings than mel cepstral distortion and a recent mean opinion score prediction model. Also, they are effective in noisy speech evaluation and have cross-lingual applicability.